Calculus 1

MATH6100 Calculus 1

The slope of a horizontal line is	0
Sketch the lines X=1, x=2, and x=3 tangent to the curve given in figure 7. Estimate the slope of each of the tangent lines you drew.	(2 answers) The slope of the tangent line x=2 is 0. The slope of the tangent lines at x=1 is 1 and at x=3 is -1.
The slope of the tangent line is called the	Derivative
The 2 divisions of Calculus are:	Integral Differential
The process of taking the limit of a sum of little quantities is called	Integration
The following problems could be solved by differential calculus:	largest or smallest volume of a solid rate or speed
Calculus was developed by Leibniz and	Newton
If a tangent line is inclined 45 degrees, then what is the slope the tangent line?	1
Find the equation of a circle with radius=6 and center C(2,-5). (write the required exponent after the ^ symbol; write the numerical coefficient of each term to complete the required equation)	X ^ 2 + y ^ 2 – 4 x + 10 y – 7 = 0
Find the slope and midpoint of the line segment from P(2,-3) to Q(2+n,-3+5n).	Slope = 5 midpoint (0.5n+ 2 , 2.5 n-3)
Find an equation describing all points P(x,y) equidistant from Q(-3,4) and R(1,-3). (use the general equation of a line	8 x – 14 y + 15 = 0
Find the line which goes through the point (2,-5) and is perpendicular to the line 3y-7x=2. (write the numerical coefficient of each term to complete the required equation)	3 x + 7 y + 29 = 0
Find the slope of the line which is tangent to the circle with center C(3,1) at the point P(8,13).	Slope of the tangent line = -5 / 12
Find the slope of the line passing through the points (3,-4) and (-6,9). Use decimal value for your final answer.	-1.44
Find the length and midpoint of the interval from x=9 to x=-2. (use decimal values for fractional answer)	Length = 11 and midpoint = 3.5
Find the equation of the line which goes through the point (3,10) and is parallel to the line 7x-y=1.	7 x – y – 11 = 0
Find the equation of the line passing through (-2,3) and perpendicular to the line 4x=9-2y. Use the general equation of the line for your final answer.	X – 2 y + 8 = 0
The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=10 to t=30 seconds?	a) average velocity = 10 feet/second
(b) What was the average velocity of the car from t=20 to t=25 seconds?	(b) average velocity = -20 feet/second
The figure shows the temperature during a day in a place. How fast is the temperature changing from 1:00 P.M. to 7:00 P.M.? Round-off your answer to 2 decimal places.	-1.67 0F/hour
From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle (a) Evaluate A(2.5)	7.5 square units
(b) Evaluate A(4) - A(1)	9 square units
For f(x) = 3x-2 and g(x) = x2+1, find the composite function defined by f o g(x) and g o f(x).	f o g(x) = 3x^2+1 g o f(x) = 9x^2-12x+5
Refer to the figure. Which of the following represents the graph drawn in red? Select one:	g(x)-1
An enrollment slip indicates a specific down payment based from the number of units enrolled by a student as follows: for number of units from 1 to 9, down payment is Php 5000; for number of units from 10 to 15, down payment is Php 10,000; and a down payment of Php 15,000 for units from 16 to 21. Which of the multiline functions define E(d), the down payment due on specific number of units enrolled. Unit is of integer type
Evaluate f(3), g(-1), and h(4)	f(3) =  1 g(-1) = -2 h(4) = 1
After evaluating g(-4), g(-1) and g(3), choose which graph represents the given conditions.
A state has just adopted the following state income tax system: no tax on the first $10,000 earned, 1% of the next $10,000 earned, 2% of the next $20,000 earned, and 3% of all additional earnings. Write a multiline function for T(x), the state income tax due on earnings of x dollars.
Given g(x) = (x+3)/(x-1). Evaluate g(5) and g(2n+1).	g(5) = 2 g(2n+1) = 1+(2/n)
A function f is given by f(7-11x) = 3x3 - 10x. Evaluate f(-4).	f(-4) = -7
A __ assigns a unique output element in the range to each input element from the domain.	function
For y=f(x),	x is the domain, and y is the range
Given f(x) = x3 - 4x2 +2, f(2) when evaluated is	-6
Which of the following figures represents the graph of a function?	Figure 2
Let f(x) = 3x+2 and g(x) = 2x+A. Find a value for A so that f(g(x)) = g(f(x)).	f(g(x)) = 6x+3A+2 g(f(x)) = 6x+A+4 A = 1
For f(x) = |9-x| and g(x) = sqrt(x-1). Evaluate fog(1).	f(g(1) = 9
Given the function f(x)=3x-4, evaluate: (a) f(x-2), (b) f(x)-f(2), (c) f(1)/f(3), and (d) f(1/3). Use fraction as final answer, if any.	(a)  3x-10 (b)  3x-6 (c)  -1/5 (d)  -3
Find the slope of the line through (0,0) and (x-1, x2 -1).	m = x+1
From the figure shown, find the values of f(2), f(-1) and f(0).	f(2) = 5 f(-1) = 2 f(0) = 1
From the graph shown, find the values of f(-3), f(-1), f(0), and f(1).	f(-3) =  -1 f(-1) = 1 f(0) = 0 f(1) =  1
Let f(x) = -x 4 -x-1, evaluate f(-1) and -2f(1).	f(-1) = -1 -2f(1) = 6
What values of x will make the statement x+5=3 or x2=9.	x = -2 or  (x = 3 and x = -3 )
What is the slope of the line through (3,9) and (x,y) for y=x2 and x=2.97? x=3.001? x=3+h? What happens to this last slope when h is very small (close to 0)? Round-off your answers to 2 decimal places, whenever possible.	Slope at x=2.97 = 5.97 Slope at x=3.001 =  6.00 Slope at x=3+h = 6+h Slope when h is close to 0 = 6
What is the slope of the line through (2,4) and (x,y) for y = x2+ x - 2 and x=1.99? x=2.004? x=2+h. What happens to this last slope when h is very small?	when x=1.99: m = 4.99 when x=2.004: m = 5.00 when x=2+h:m = 5+h when h approaches 0: m = 5
What is the slope of the line through (-1,-2) and (x,y) for y = x2+ 2x + 1 and x=-0.90? x=-1.05? x=h1? What happens to this last slope when h is very small? Round-off your answers to 2 decimal places whenever possible. Use the ^ symbol to express the exponent of a variable, i.e. x^2 (x squared)	when x=-0.90: m =  2 when x=-1.05: m =  3.3 when x=h-1: m = h^2+1 /h when h approaches 0: m = 1
The figure shows the distance of a car from a measuring position located on the edge of a straight road. (a) What was the average velocity of the car from t=0 to t= 20 sec? (b) What was the average velocity from t=10 to t=30 sec? (c) About how fast was the car traveling at t=15 sec?	(a) V = 15 ft/sec (b) V = -5 ft/sec (c) V = 20 ft/sec
Define A(x) to be the area bounded by x and y axes, the line y=x+1, and the vertical line at x. (a) Evaluate A(2) and A(3) (b) What area would A(3) - A(1) represent?	(a) A(2) = 4 square units A(3) = 7.5 square units (b) A(3) - A(1) = 6 square units
The graph shows the population growth of bacteria on a petri plate. If at t=10 days, the population grows to 4600 bacteria, find the rate of population growth from t=9 to t= 10 days?	rate of growth = 400
Write the contrapositive of the statement: If x2 + x - 6 = 0 then x=2 or x=-3.	Answer: If x = - 2 and x = 3 then x2 + x - 6 is not equal to 0
The slope of the line through (5,15) and (x+8, x2 -2x) is	x-5
Given g(t) = t+5t−1t+5t−1, evaluate: (a) g(5) and (b) g(2s - 5)	(a) g(5) = 5/2 (b) g(2s-5) = s/s-3
Let f(x) = -x 4 -x-1, evaluate f(-1) and -2f(1).	f(-1) = -1 -2f(1) =  6
Let f(x)=-1-x-2x2 , evaluate f(x+h)−f(x)hf(x+h)−f(x)h Factor out the negative sign for the final answer, if any	-(4x+2h+1)
Which of the following are negation of the statement: f(x) and g(x) are polynomials.	f(x) or g(x) is a polynomial f(x) and g(x) are not polynomials
Find the slope of the line through (-5,3) and (x+1, x-2).	x-5/x+6
Write the contrapositive of the statement: If x>3, then x2>9. Use words or phrase for your answer.	If x2 <= 9, then x <= 3
Let f(x) = 2-x 2 , evaluate (a) f(x+1) and (b) f(x)+f(1)	(a) f(x=1) = -x 2 - 2x+1 (b) f(x) + f(1) = -x 2+3
If a and b are real numbers, then (a+b)2 = a2+b2 .	False
Which of the following is the contrapositive for the statement: If your car is properly tuned, it will get at least 24 miles per gallon.	If your car will not get at least 24 miles per gallon, then it is not properly tuned.
If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function	True
Let f(x)=1-(x-3)2 , evaluate: (a) f(x+3), (b) f(3-x), and (c) f(2x+1).	(a) 1 - x 2 (b) 1 - x 2 (c) -4 x 2 + 8x-3
Which of the following will make the statement x2+3 > 1 true?	x is greater than or equal to -1
Let f(x) = 1-(x-1)2 evaluate (a)f(2)f(3) and (b)f(23)(a)f(2)f(3) and (b)f(23	(a) Answer 0 (b) Answer 8/9
Let f(x) = 2-x 2 , evaluate (a) f(x+1) and (b) f(x)+f(1).	(a) f(x=1) = -x 2 - 2x+1 (b) f(x) + f(1) = -x 2+ 3
Find the slope of the line through (-3-1) and (x+3, y+1).	x-5/x+6
From the graph shown, find: a. f(-1) b. f(0) c. 3f(2) d. the value of x that corresponds to f(x)=0	a. f(-1) = 2 b. f(0) = 1 c. 3f(2) = -14 d. x = 0
Let A = {1,2,3,4,5}, B = {0,2,4,6}, and C = {-2,-1,0,1,2,3}. Which of the values of x will satisfy each statement?	x is in A or x is in C
Find the slope of the line through (0,0) and (x-1, x2	m = x+1
Which graph corresponds to f(x) = √x?
Which graph represents the function f(x) = {2 if x ≤ -1} {x2 if x > -1}
Evaluate limx→0cos2x−1cosx−1limx→0cos2x−1cosx−1	4
Write the contrapositive of the statement: I feel good when I jog. Answer: When I don't jog, I feel	Bad
Evaluate limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3	108 / 7
Write the negation of the statement: 8 is a prime number. 8 is	not a prime number
Evaluate limx→1x13−1x14−1limx→1x13−1x14−1	4 / 3
Evaluate limx→103x−5−−−−−√5limx→103x−55	1
Every vertical line on the Cartesian plane intersects the x-axis.	True
Evaluate limx→43−x+5−−−−√x−4limx→43−x+5x−4	1 / 5
Evaluate limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5	2
Which values of x will make the statement x+5=3 or x2=9 true?	-2 or (3 and -3)
The sum of two prime numbers is a prime.	false
Use the function h defined by the graph shown to determine the following limits: (a) limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3)	(a) 1 (b) -2
At which values of x is the function f(x)=x2+x−6x−2f(x)=x2+x−6x−2continuous and discontinuous?	continuous at x = -3 discontinuous at x = 2
Use the function h defined by the graph below to determine the following limits: (a) limx→2x+h(x)limx→2x+h(x) b) limx→3h(x2)	(a) 3 (b) 3/4
Use the graph below to determine the right-hand limit of the function f(x) at: (a) x=-2 (b) x=10	(a) undefined (b) 0
Use the functions f and g defined by the graphs as shown to determine the following limits: (a) limx→1(f(x)xg(x))limx→1(f(x)xg(x)) (b) limx→1f(g(x))	(a)  0 (b)  5/4
hich values of x is the function from the graph shown continuous? State the answers from the least to the highest, if there would be more than one	x = -1
Use the function f defined by the graph shown to determine the following limits: (a) limx→1+f(x)limx→1+f(x) (b) limx→1−f(x)	(a) 2 (b) -1
Use the Bisection Algorithm Method to find the root of the given function to an interval of length less than or equal to 0.1. Answer should be up to one decimal place only. f(x) = x2 - 2 on [0,3]	1 / 4
(a) limx→2h(2x−2)limx→2h(2x−2) (b) limx→2h(1+x)	(a) 1 (b) 1
Use linear equation to estimate e0.06 . Choose a value of 'a' to produce a small error.	e 0.06 = 1.06
Determine all the critical points for the function. f(x)=xex2	does not have any critical points
Determine whether the graph is continuous or not continuous.	Not Continuous
There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees?	x = 15 additional trees P =r 42250 apples
Use chain rule to calculate dydxdydx of y=sin(4x3+3x+1)y=sin(4x3+3x+1)	dydx=(12x2+3)cos(4x3+3x+1)dydx=(12x2+3)cos(4x3+3x+1)
Find a value for B so that the line y = 10x – B, goes through the point (5,-5).	B = 55
For all positive real numbers a and b, if a > b, then a2 > b2	TRUE
Determine whether the graph is continuous or not continuous.	Continuous
You are standing at the edge of a slow-moving river which is one mile wide and wish to return to your campground on the opposite side of the river. You can swim at 2 mph and walk at 3 mph. You must first swim across the river to any point on the opposite bank. From there walk to the campground, which is one mile from the point directly across the river from where you start your swim. What route will take the least amount of time?	x ≈ 0.89 mi. Shortest possible time: T ≈  0.71 hr.
Determine whether the graph is continuous or not continuous.	Not Continuous
Find an equation of the line tangent to the graph of x2+(y−x)3=9x2+(y−x)3=9 at x=1	y=76x+136y=76x+136
Use linear approximations to estimate 1–√46146. Choose a value of "a" to produce a small error	1–√46=f(146)≈L(146)146=f(146)≈L(146) = 12.08
Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.	r ≈ 1.89 h ≈ 2.67 V ≈ 9.93
Find the slope and concavity of the graph pf x2y+y4=4+2xx2y+y4=4+2x at the point (-1,1)	Slope = 4545, Concavity = downward
A container in the shape of a right circular cylinder with no top has surface area 3 ft.2 What height h and base radius r will maximize the volume of the cylinder?	r = 1 ft. h = 1 ft. V = 3.14 ft3
If a and b are real numbers then (a + b)2 = a2 + b2	False
Assume that y is a function of x. Find y1=dydxy1=dydx for cos2x+cos2y=cos(2x+2y)cos2x+cos2y=cos(2x+2y)	y1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysinyy1=cosxsinx−sin(2x+2y)sin(2x+2y)−cosysiny
Find a linear approximation to h(t)=t4−6t3+3t−7h(t)=t4−6t3+3t−7 at t=−3t=−3.	L(t) = 227 - 267 (t + 3) = -267 t -  57
Find the local extreme values of the given function: f(x)=x4−6x2f(x)=x4−6x2	Local minimum: (-1.73, -9) Local maximum:(1.73, -9)
Use chain rule to calculate dydxdydx of y = tan (e3x√)(e3x)	dydx=−sec2(e3x−−√)3e3x√23x−−√dydx=−sec2(e3x)3e3x23x
Use chain rule to calculate dydxdydx of y=cos4(7x3)y=cos4(7x3)	dydx=−84x2cos3(7x3)sin(7x3)dydx=−84x2cos3(7x3)sin(7x3)
(\Large \lim_{x \rightarrow 3} (2x + 1) = 7 \) What values of x guarantee that f(x) = 2x + 1 is within 0.04 units of 7? If x is within ­­­­­­_____ units of 3, then f(x) is within 0.04 units of 7.	0.02
Find the point of intersection and the angle between x - y = 32 and 3x - 8y = 6.	Point of Intersection = (50 , 18 ) Angle of Intersection = -24.44 0 (round-off to 2 decimal places)
If f(x) and g(x) are linear functions then f(x)g(x) is a linear function.	False
Use the function h defined by the graph below to determine the following limits: (a) limx→2(xlimx→2(x . h(x−1))h(x−1)) (b) limx→0h(3+x)−h(3)h(x)limx→0h(3+x)−h(3)h(x)	(a)  8/3 (b)  -6/5
Determine all the critical points for the function. f(x)=x2ln(3x)+6f(x)=x2ln(3x)+6	0.20
Write the contrapositive of the statement: If I exercise and eat right, then I will be healthy. Don't use contractions in your answer	If I  am not healthy, then I do not exercise and eat right.
Which of the following equations is the line perpendicular to 2x – 3y = 9?	3x + 2y =10
Determine whether the graph is continuous or not continuous.	Continuous
Given a function f, an interval [a,b] and a value V. Find a value c in the interval so that f(c)=V. Apply the Intermediate Value Theorem. (a)f(x)=x2f(x)=x2 on [0,3], V = 2 (b)f(x)=sinx on [0,π2],V=12f(x)=sinx on [0,π2],V=12	(a) c = -1.41 ; c = 1.41 (b) c = 0.52
Evaluate limx→3x4−812x2−5x−3limx→3x4−812x2−5x−3	108 / 7
Find an equation of the line tangent to the graph of y=x2+sinπ2xy=x2+sinπ2x at x = -1	y = -2x - 2
Use implicit differentiation to finddydxdydx exy=2yexy=2y	y1=yexy2−xexyy1=yexy2−xexy
(Note: Answers should be in decimal form. Up to two decimal places only)	x = 1.5 Smallest sum: S = 8.5
Which of the following equations is the line perpendicular to 4y – 7x = 5?	4x + 7y – 18 = 0
1. Write the equation of the line that represents the linear approximation to the function below at a given point a. f(x) = ln(1 + x); a = 0; f(0.9)	y = L(x) = x
2. Use linear approximation to estimate the given function value.	f(0.9) = 0.9
. Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact	Percent error: 40.22 %
The slope of the line from point U(5,13) and the point V(x+1, x2 -3) is	x+4
Use chain rule to calculate dydxdydx of y=x2sec(5x)y=x2sec(5x)	dydx=−2xsec(5x)+5x2sec(5x)tan(5x)dydx=−2xsec(5x)+5x2sec(5x)tan(5x)
Let f(x) = (x-1)2 and define S(x) to be the slope of the line through the point (0,0) and (x,f(x)). Evaluate S(6).	S(6) = 25/6
(Note: Answers should be in decimal form only. Up to two decimal places}	x ≈ 8.77 ft. y ≈ 16.67 ft. L ≈ 17.64 ft.
Evaluate limx→0(x+1)3−1xlimx→0(x+1)3−1x	3
Fill in the missing the numbers to find the correct answer/s: Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum. P = xy2	x = 3 y = 6 P =  108
If f(x) and g(x) are linear functions, then f(x) + g(x) is a linear function.	True
Use Newton's Method to find the root of 2x2+5=ex2x2+5=ex accurate to six decimal places in the interval [3,4].	x ≈ 4.36
(Note: Answer should be in decimal form. Up to two decimal places only)	x ≈ 17.32 ft. θ = 30 degrees
Determine whether the graph is continuous or not continuous.	Continuous
limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5?	If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5.
Determine all the critical points for the function y=6x−4cos(3x)y=6x−4cos(3x) x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,... x=???+2πn3,n=0,±1,±2,...x=???+2πn3,n=0,±1,±2,...	1.2217; 1.9199
Assume that y is a function of x. Find y1=dydxy1=dydx for x−y3y+x2=x+2x−y3y+x2=x+2	y1=1−y−3x2−4x3y2+x+2y1=1−y−3x2−4x3y2+x+2
Evaluate limx→0(x+5)2−25xlimx→0(x+5)2−25x	10
Evaluate limx→35x2−8x−13x2−5limx→35x2−8x−13x2−5	2
Write the equation of the line that represents the linear approximation to the function below at the given point a. f(x)=e2;a=0;f(0.05)f(x)=e2;a=0;f(0.05)	f(a) = 7.39
Use the linear approximation to estimate the given function value.	f(0.05) ≈ L (0.05) = 0.05
Percent error ≈	20
Given f(x) = 2x + 3 and g(x) = x2 . Evaluate . Sample text answer: 3x^2+6x7. Do not use space between the number, letter and symbol.	4x^2+12x+9
Use Newton's Method to determine x2x2 for f(x)=xcos(x)−x2f(x)=xcos(x)−x2 if x0=1x0=1	x2 =  0.74
Assume that y is a function of x. Find y1=dydxy1=dydx for (x−y)2=x+y−1(x−y)2=x+y−1	y1=2y−2x+12y−2x−1y1=2y−2x+12y−2x−1
Use chain rule to calculate dydxdydx of y=e−x2y=e−x2	dydx=−2x−x2dydx=−2x−x2
Locate the critical points of the following functions. Then use the second derivative test to determine whether they correspond to local minima or local maxima or whether the test is inconclusive.	Critical points: (2, -1/4) and (10, -1/20) Local minimum: x = -2 Local maximum: x = 10
Use Newton's Method to find the root of x4−5x3+9x+3=0x4−5x3+9x+3=0 accurate to six decimal places in the interval [4,6].	x ≈ 4.53
Identify the absolute extrema and relative extrama for the following function. f(x)=x3f(x)=x3 on [-2,2]	The function has an absolute maximum of 8 at x = 2 and absolute minimum of -8 at x = - 2. The function has no relative extrema.
Use the functions f and g defined by the graphs as shown to determine the following limits: (a) limx→1f(x)+g(x)limx→1f(x)+g(x) (b) limx→2f(x)g(x)limx→2f(x)g(x)	(a) 2 (b) 4/3
Determine whether the graph is continuous or not continuous.	Not Continuous
Use implicit differentiation to find dydxdydx (xy+1)3=x−y2+8(xy+1)3=x−y2+8	y1=1−3y(xy+1)23x(xy+1)2+2yy1=1−3y(xy+1)23x(xy+1)2+2y
Evaluate limx→7x−3−−−−√limx→7x−3	2
Build a rectangular pen with three parallel partitions using 500 feet of fencing. What dimensions will maximize the total area of the pen?	x = 50 ft. y = 125 ft. A = 6250 ft2
For the function f(x)=x(x2+1)2f(x)=x(x2+1)2 on [-2,2] Find the critical points and the absolute extreme values of f on the given interval.	x=±13−−√x=±13 as the critical points absolute maximum value of f: 33√163316 absolute minimum value of f:33√163316
Assume that y is a function of x. Find y1=dydxy1=dydx for y=x2y3+x3y2y=x2y3+x3y2	y1=2xy3+3x2y21−3x2y2−2x3yy1=2xy3+3x2y21−3x2y2−2x3y
limx→13x+2=5limx→13x+2=5 What values of x guarantee that f(x) = 3x + 2 is within 0.05 unit of 5?	If x is within 0.02 unit distance of 1, then f(x) is within 0.05 unit of 5
An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions will result in a box with the largest possible volume?	x = 4 ft. y = 2 ft. V = 32 ft.3
Write the negation for the statement: All quadratic equations have solutions.	not all quadratic equations all solutions.
Use the function h defined by the graph shown to determine the following limits: (a) limx→2h(5−x)limx→2h(5−x) (b) limx→0h(3+x)−h(3)limx→0h(3+x)−h(3	(a) 3 (b) 3/4
Use implicit differentiation to find dydxdydx, x3=x+yx−yx3=x+yx−y	y1=3x2(x−y)2+2y2xy1=3x2(x−y)2+2y2x
Find the point of intersection and the angle between y = 4 - 2x and x - y = -1.	Point of Intersection = (1 , 2 ) Angle of Intersection = -71.56 0
Find a linear approximation of f(x)=3xe2x−10f(x)=3xe2x−10 at x = 5	L(x) = 15 + 33 (x - 5) = 33 x + 150
Determine whether the graph is continuous or not continuous.	Continuous
Find the point of intersection and the angle between 2x - 3y = 3 and 4x - 2y = 10.	Point of Intersection = (3 , 1 ) Angle of Intersection = 29.740
Consider a rectangle of perimeter 12 inches. Form a cylinder by revolving this rectangle about one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume?	r = 4 ft h = 2 ft V ≈ 100.53 ft3
Evaluate limx→43−x+5−−−−√x−4limx→43−x+5x−4	- 1 / 6
Use chain rule to calculate dydxdydx of y=(5x2+11x)20y=(5x2+11x)20	dydx=(20)(5x2+11x)19(10x+11)dydx=(20)(5x2+11x)19(10x+11)
Determine whether the graph is continuous or not continuous.	Not Continuous
Evaluate limx→103x−5−−−−−√5limx→103x−55	1
Which of the following are integer values of x that will make the statement x>4 and x	5,6,7,8
Determine whether the graph is continuous or not continuous.	Not Continuous
If x divides 49, then x divides 30.	False
Every straight line on the Cartesian plane intersects the x-axis.	True
Assume that y is a function of x. Find y1=dydxy1=dydx for y=sin(3x+4y)y=sin(3x+4y)	y1=3cos(3x+4y)1−4cos(3x+4y)y1=3cos(3x+4y)1−4cos(3x+4y)
Do the following. Determine the answers by typing the missing numbers on the spaces provided. Up to two decimal places only:
f(x) = 12 - x 2 ; a = 2 ; f(2.1)	L(x) = -4 x + 16
Use linear approximation to estimate the given function value	f(2.1) = 7.6
Compute the percent error in your approximation by the formula: |approx−exact|exact|approx−exact|exact	Percent error is: 0.13 %
(Note: Answers should be in decimal form. Up to two decimal places only)	Largest possible slope: x = 1 y = 1.5 S =  -0.75 Smallest possible slope: x =  -1 y = -1.5 S = 0.75
Find an equation of the line tangent to the graph of (x2+y2)3=8x2y2(x2+y2)3=8x2y2 at the point (-1,1)	y - 1 = x + 2
A sheet of cardboard 3 ft. by 4 ft. will be made into a box by cutting equal-sized squares from each corner and folding up the four edges. Given that variable x shall be the length of one edge of the square cu from each corner of the sheet of cardboard, what will be the dimensions of the box with largest volume?	x ≈ 0.57 ft, so Length = 2.86 ft Width = 1.86 ft Height = 0.57 ft V ≈ 3.03 ft
Given f(x) = 2x + 3. Evaluate (f°f)(x). Sample text answer: 3x^2+6x-7. Do not use space between the number, letter and symbol.	4x+9