Calculus Questions

Find the interval s of numbers that are at least a distance of 8 away from 7 Enter solution as an interval or union of intervals inf 15 U 15 inf A help intervals In absolute value notation where x represents the numbers this is A x 81 7 B x 812 7 C x 7 8 D x 7 8 E None of the above

a The graph of a function y f x is horizontally compressed by a factor of 4 Find an equation for this compressed function in terms of the function f x For example y 10f 9x 8 7 help equations b The graph of the function y e 10 is horizontally compressed by a factor of 4 Find an equation for this compressed function help equations c The graph of a function y g z is horizontally expanded by a factor of 9 Find an equation for this expanded function in terms of the function g x For example y 10g 9z 8 7 help equations d The graph of the function y 2 2z is horizontally expanded by a factor of 9 Find an equation for this expanded function help equations

Starting graph a shifting f x 3 units upward y 9x 3 b shifting f x 2 units to the right y 9x 2 c reflecting f x about the x axis y 9x d reflecting f x about the line y 2 y 9x 2 gid

8 5 points Let f t describe the temperature in degrees Fahrenheit of a cup of coffee t minutes after it has been brewed a 2 points What are the units of f t b 3 points Give an interpretation of the following mathematical expressions in the context of this problem for a non mathematical friend i f 0 200 ii f 0 10 iii f 0 0

5 8 points Consider the function 2 f x 2 i f 2 ii lim f x x 2 x 2 os TX k where k is a fixed constant The following is a graph for the function f x when k 3x if x 2 if x 2 MAMA a 4 points Use the graph above to determine the following If a limit does not exist write DNE iii lim f x x 2 10 iv lim f x x 2 b 2 points Find a value of k for which f x is continuous everywhere

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stion 5 Write an equation for the quadratic graphed below x intercepts 2 0 and 3 0 y intercept 0 2 2 3 Q

Question 9 A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in squares from each corner and folding up the sides The box is to hold 11552 in How big a piece of cardboard is needed Your answer is in by Question Help Video Message instructor in

Question 4 Find b and c so that y 7x bx c has vertex 9 8 b C

Consider the parabola given by the equation f x 4x 10x 10 Find the following for this parabola A The vertex B The vertical intercept is the point C Find the coordinates of the two a intercepts of the parabola and write them as a list separated by commas It is OK to round your value s to to two decimal places

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Question 3 b What is the y intercept The graph of f x 4 is reflected about the y axis and shifted upward 4 units a What is the equation of the new function g x g x c What is the domain d What is the range Question Help VIDEO Post to forum

The Kardashi B O A Failed to ope B f x 4 0 66 8 f x 2 0 66 e f x 4 1 32 a f x 2 0 89 e f x 2 1 32 8 f z 2 1 58 AC a A b B C C d D e E f F New Apple iP D Weedmaps E F Welcom

Score 0 42 0 10 answered Question 2 Start with the graph of f x 2 Then write a function that results from the given transformation Reflect f x about the y axis g x Question Help VIDEO Post to forum

Find the equation of the tangent line to the curve y 6x cos x at the point 7 6 The equation of this tangent line can be written in the form y mx b Compute m and b m EEB

2 Some values of a differentiable function f x and its derivative f x are given in the table below X 0 1 2 3 4 28 f x 0 5 3 0 5 3 1 5 3 2 f x 1 2 4 r f x a 6 points Compute g 1 where g x f x f t 2t dt Simplify your final answer

Use the figures below to evaluate the indicated derivative or state that it does not exist If the derivative does not exist enter dne in the answer blank The graph to the left in black gives f x while the graph to the right gives g x which is constant for values of a greater than 40 200 200 40 40 0 40 10 0 168 40 f g x 20 If the derivative does not exist enter dne 40 0 40 40 0 g x 168

A table of values for f g f and g is given below a If F x f f x find F 2 b If G x g g x find G 3 a F 2 b G 3 E x f x g x x g x 6 7 9 123 2 317 7 282 57 7

Consider the function r x f g h x Given that h 1 4 h 1 5 g 5 3 Find the value of r 1 or enter NA if there is not enough information to compute this derivative r 1 g 5 6 and 6 2

Find y if y e 1 z

Find the derivative of Assume that a and b are constants h x 5 b h

Let f x 12 sin x 9 cos x

4 The graph of a function g is shown on the zy plane on the interval 7 7 A table of selected values is given for a different function h which has only one a real zero H h z 5 2 2 7 3 0 13 7 20 0 2 4 Let f x 2g x 3h x Find f 4 b Let j x g x h a How many a intercepts does j have on the interval 7 7 c Let k x M g x h x Which values are restricted from the domain of k Explain X g x y

6 Let f x x2 16 and g x 2x 9 a What is the domain of f What is the domain of g b Find g x f x c What is the domain of 9 2 f x

7 Let h a 25 2 and j x 7x 1 a What is the domain of h x b What is the domain of j x c Let k x h x j x What is the domain of k x 2 h 2 What is the domain of f x d Let f x

6 15 pts The average price C of Oreo Cookies was 2 69 lb in 1990 and 3 00 lb in 2018 Assume that the exponential growth model applies a Find the exponential growth rate in 5 decimal places b Find the exponential function that models this situation c What will the price of 1 lb of Oreo Cookies be in 2025 d Find the rate of change of the price of 1 lb of Oreo Cookies in 2025 and explain what this rate means

Show all the necessary steps for full credit 1 10 pts Use the graph to find the following limits and function value Ay 175 10 15 15 X INO a b C d e f 2 f 7 lim f x X 7 lim x x 2 lim f x X 2

1 10 pts Use the graph to find the following limits and function value 10 10 5 5 LO 10 5 10 a b C d e f 2 7 lim f x x 7 lim f x x 2 lim f x x 2

QUESTION 5 points Find the derivative of y 2x 1 x 3 4

2 17 pts Use limit properties algebraic simplification tables of values and or graphs to find each limit if it exists If you are using a table of values or a graph make sure you include the table of values or the graph If the limit does not exist explain why and be descriptive as possible x 2x 24 x 6 x 12x 36 a lim x 2x 24 b lim x 3x 8x 16 c lim 4 r 3 x 3

4 8 points Find the 2nd derivative of the following function Write the final answer in exponential notation using only positive exponents f x 5x 1

3 40 pts Find the derivative of the following functions a f x 4x 2x 0 4x 2x b f x el In 2x 3x c y d y x 2 ln x e F x x e x 2e

9 points Use the information below to sketch the graph for f x on the interval 2 x 2 Label any points on the x axis or y axis which are important Note Precision in drawing is not required as long as it is clear from the graph what you intended to do be careful that your graph is visibly curved where it is supposed to be curved f x 0 for x 1 f x 0 for x 0 f 1 0 f x 0 for 1 x 1 f 1 0 f x 0 for x 1 f 0 0 f x 0 for 0 x 1 f x 0 for x 1 2

During the winter if the low temperature outside is a C the daily cost to heat a building can be determined using the function f x 6 1 3 Find and interpret the given function values and determine an appropriate domain for the function Round all function values to the nearest hundredth Answer Attempt 1 out of 2 f 6 meaning when the low temperature outside is interpretation f 9 interpretation f 4 5 interpretation in the context of the problem meaning when the low temperature outside is V in the context of the problem meaning when the low temperature outside is C it would cost C it would cost in the context of the problem C it would cost Based on the observations above it is clear that an appropriate domain for the function is to heat the building This to heat the building This to heat the building This

When an airplane leaves the runway its angle of climb is 170 and its speed is 275 feet per second Find the plane s altitude after 1 minute Round your answer to the nearest whole number X ft

Solve the right triangle shown in the figure Round your answers to two decimal places A B 82 2 C 90 a b C 186 15 B a 7 8 C 25 5 X b 0 O

Given the parametric equations Write the derivative dy dx as a function of t x 2t 4 y sin 3t

A sign on the roadway at the top of a mountain indicates that for the next 4 miles the grade is 9 5 see figure Find the change in elevation for a car descending the 4 mile stretch Round your answer to two decimal places mi mi Not drawn we

4 of 10 4 5 points Starting from a stop a mouse runs to the right first then comes to a stop for a few seconds and then runs to the left Consider the graphs below Graph A Graph C Graph B a 2 points Which of the above graphs could describe the position of the mouse as a function of time b 2 points Which of the above graphs could describe the velocity of the mouse as a function of time c 1 point Based on the graphs that you have chosen in the previous parts Is the mouse accelerating decelerating or neither at the beginning

An observer in a lighthouse 350 feet above sea level observes two ships directly offshore The angles of depression to the ships are 6 and 0 9 5 see figure How far apart are the ships Round your answer t decimal place 350 ft

When an airplane leaves the runway its angle of climb is 17 and its speed is 275 feet per second Find the plane s altitude after 1 minute Round your answer to the nearest whole number ft

From a point x 110 feet in front of a public library the angles of elevation to the base of the flagpole and the top of the flagpole are 0 28 roof Find the height of the flagpole aft STEP 1 Let F be the height of the flagpole and L be the height of the public library Convert the angle 39 45 into decimal form Use this value and an appropriate trigonometric function to find F L the total height of the library and flagpole feet F L STEP 2 Find the height of the library L LI feet STEP 3 Subtract your result from Step 2 from your latter result in Step 1 to determine the height of the flagpole F F feet Need Help Read

When an airplane leaves the runway its angle of climb is 14 and its speed is 275 feet per second How long will it take the plane to climb to an altitude of 10 000 feet 16 000 feet Round your answers to one decima place 10 000 ft 16 000 ft S S

A cadet rappelling down a cliff on a rope needs help A cadet on the ground pulls tight on the end of the rope that hangs down from the rappelling cadet to lock the cadet in place The length of the rope between the t cadets is 143 feet and the angle of elevation of the rope is 70 How high above the ground is the cadet on the rope Round your answer to two decimal places ft

Consider the following equation 1000 5 102 Which of the following equations can be used to find the value of t O A log10 1000 5 2t OB log10 200 2t log2 1000 5 10t log 200 10t C D

Find the quotient and remainder using synthetic division 6x x x 1 quotient

63 66 Solve each equation for x 63 a e7 4x 6 b

A graphing calculator is recommended A cardboard box has a square base with each edge of the base having length x inches as shown in the figure The total length of all 12 edges of the box is 144 in X a Express the volume V of the box as a function of x V x

Find the quotient and remainder using synthetic division xx x x 2 X 2 quotient remainder

Select all that apply 5 2 500 Calculate E 2 where E is the elasticity of demand and select the correct interpretations of the result When p When p P X When p 2 the elasticity of demand satisfies E 2 1 which is elastic 2 the elasticity of demand satisfies E 2 1 which is inelastic When p 2 an increase in price will result in increased revenue 2 an increase in price will result in decreased revenue