Calculus Questions

Evaluate the integral using an appropriate substitution x x8 5 dx C

Evaluate the integral using an appropriate substitution x 1 x 2x dx C

Evaluate the indefinite integral Inx dx 7 c x S

Find the area of the figure A V 4 m 15 m 13 m 6 m

Find the area of the figure A Simplify your answer 12 m 26 m 48 m 26 m 12 m 22 m

34 2 1 4 3 2 1 H 2 1 2 3 4 5 6

7 Let M t represent the rate at which people enter Macy s department store in people per hour t hours into their Black Friday sale Interpret the statement M 3 5 432 in the context of this problem

1 Determine if each of the following relationships can be represented with a function f where f z y Give a reason for your answer a A child s height in inches y on their birthday at age z b month of the year y average weekly price of gas at a gas station c The cost of mailing a small package y based on its weight z

3 Let L t represent the number of likes on a social media post t hours after it is posted Interpret the statement L 4 2L 3

6 The graph of y g a is shown Order the following from least to greatest g 1 g 2 g 0 5 g 2 5 5 4 0 1 2

3 A table of selected values is given for a function f f x 11 8 3 4 2 X 5 2 120 7 a Find f 2 h What is the value of when f x

5 The graph of y g a is shown For which value s of is 9 0 0 4

2 Let h x x 3x 6 Find the following values a h 3 b h 2

4 The graph of y 9 a is shown Find g 1 76 yol 5

19 a Find and interpret C 15 20n if 1 n 30 if 30 n 45 C n 15 50n 10n if n 45 21 b How much does it cost to order 45 copies of the book What about 46 copies 22 Your answer to 19b should get you thinking Suppose a bookstore estimates it will sell 45 copies of the book How many books can in fact be ordered for the same price as those 45 copies Round your answer to a whole number of books 0 An on line clothing retailer charges shipping costs according to the following formula 55 SC

ph the function f x 4x and draw the tangent lines to the graph at points whose x coordinates are 0 and 1 4 40 8 7 6 5 o 9 10 H 42 13 44 45 16 7

Next question 5 4 3 2 1 ich 3 2 2 3 4 2 3 Get a similar question er You can retry this question Determine the intervals where the derivative of this graph is positive and negative Use interval notation Positive derivative on the interval s 2 1 5

y 5 x y x 5 y x 5 y 5x y x 5 2 2 y x 5 y 5x 2 y 5 x y x 5 y x 5 y x 5 y x 5 Drag the function given above into the appropriate area below to ma Ay M Ay 0

Starting with the graph of a basic function graph the following function using the techniques of shifting compressing stretching and or reflecting Find the domain and range of the function g x 5 x 4 2 Use the graphing tool to graph the equation Click to enlarge graph 10 B 6 4 2 10 8 6 2 2 4 6 2

1 Evaluate arcsin 3 and cos 2 8

52 Let P x F x G x and Q x F x G x where F and G are the functions whose graphs are shown a Find P 2 b Find Q 7 1 0 G

Open the picture named Number Line 1 and recreate the number line going from 3 on the far left to positive 3 on the far right Place the word mean in the center of your number line Now open the picture named Number Line 2 Notice how the calculation work is being shown for an example of show your work Notice that numbers are being placed at three spots going to the left and three to the right Your answer for each question below should include a drawn number line the numbers that would be on the number line at each point on the line three to the right and three to the left of the mean in center EXAMPLE showing detail work See pic Number Line 2 The mean of some data equals 100 units units of w e with a standard deviation of 6 units same w e Show your calculations for all six numbers on the number line three to the left and three to the right Right 100 6 106 106 6 112 112 6 118 Left 100 6 94 94 6 88 88 6 82 Here is the assignment Show detail work answering the two questions below Then create a number line for each question that represents your answer Hand in your detailed calculation work and the number lines Question 1 The mean of some data equals 98 liters with a standard deviation of 10 liters Show your calculations for all six numbers on the number line three to the left and three to the right of center Right Left Make sure and hand in a number line with your calculated results included on it just like the example 2 on next page Question 2 The mean of some data equals 18 6 pounds with a standard deviation of 1 1 pounds Show your calculations for all six numbers on the number line three to the left and three to the

Challenge yourself Domain Range x intercepts y intercept Increasing Interval s Decreasing Interval s LEB as x REB as x f x f x

Get a similar question You can retry Suppose f x is continuous over an interval a x b and a c d b 10 then check all that apply f x is decreasing through a c f does not have a maximum at x c Of does not have a minimum at x c 10 Of c f c exists f x is increasing through x c X Hint Be sure to check ALL that apply X If f d 1 then check all that apply f does not have a maximum at x d f x is increasing through x d f d 1 Of x is decreasing through x d Of does not have a minimum at x d Of d exists Hint Be sure to check ALL that apply Based on this we know that for some x between x cand x d f does not exist Of has a minimum Of has a maximum f x 0

Question 8 The figure below shows a function p x and its tangent line at the point B 4 7 3 If the point A on the tangent line is 3 66 3 312 fill in the blanks below to complete the statements about the function p at the point B p A BO

Question 5 Consider the function y f x graphed below Give the a a intervals on which the derivative of the function is negative x b intervals on which the value of the function is negative x c one x value where the derivative of the function is the least meaning most negative x d one a value where the derivative of the function is zero x

5 4 3 2 1 B 3 2 t N 3 23 A Determine the intervals where the derivative of this graph is positive and negative Use interval notation Positive derivative on the interval s Negative derivative on the interval s

Suppose that the graph of a function f is known Then the graph of y f x 2 may be obtained by a f the graph of f a distance of 2 units vertical

Next question Get a similar Suppose that f is a function given as f x 7x 5 We will compute the derivative of f at x 3 as follows First we will compute and simplify the expression f 3 h f 3 h Then we compute and simplify the difference quotient between x 3 and x 3 h f 3 h f 3 h The derivative of the function at x 3 is the limit of the difference quotient as h approaches zero f 3 h f 3 h f 3 lim h 0

Question 10 The point 15 3 lies on a differentiable function f x The tangent line to f x at x 15 also goes through the point 2 88 What is f 15 f 15

8 Next question 6 4 10 8 6 4 2 2 4 6 Clear All Draw Dot Get a similar question Line Segment 8 You can a Mark the two points on the graph that are needed to calculate Average Rate of Change over the interval 4 1 b Connect the points with a line segment c The Average Rate of Change over 4 1 is positive negative

Westside Energy charges its electric customers a base rate of 7 00 per month plus 10 per kilowatt hour kWh for the first 300 kWh used and 3 per kWh for all usage over 300 kWh Suppose a customer uses x kWh of electricity in one mont a Express the monthly cost E as a piecewise defined function of x Assume E is measured in dollars if 0 x 300 E x b Graph the function E for 0 x 600 E 40 30 20 10 O E 40 30 20 10 if 300 x 100 200 300 400 500 100 600 X 200 300 400 500 600 E 40 30 20 10 E 70 60 50 40 30 20 10 O 100 X 200 300 400 500 600 100 200 X 300 400 500 600

15 54 to find the indicated derivative 1 f 1 if f x x 3 f 3 if f t 8 1 Microsoft Teams 4 In Problems 5 22 use f x lim f x h f x h to find the derivative at x https teams microsoft com modern calling 5 s x 2x 1 7 r x 3x 4 9 f x ax bx c 11 f x x 2x 1 13 h x Latin Dals Edin Powell and tege Wed 14 132 X f c lim AD 100 9 y sin x x 11 y cos x 13 y 19 y 3x x 2 15 y cos 17 y 3x 2 3 x x 1 3x 4 24 10 12 y sin 3x 14 y 3 16 y cos 18 y 2 3x x 3 20 y 24 D Suara Anda dimatikan Tekan Ctrl Shift M untuk menyalakan suara mikrofon atau tekan dan tahan Ctrl Spacebar 2 f 2 if f t 2x 4 f 4 if f s 2x 3 x 4 In Problems 21 28 find the indicated derivative 21 y where y x 4 22 y where y x sin x Orang Angkat 6 f x ax 8 f x x x 1 10 f x x 12 g x x x 14 S x 88 Reaksi Tampilan Lainnya 39 Comment sin x 3x Sin cost 37 D cos sin 0 A Share Kamera Mikr sin cos sin 2x 4 In Problems 41 46 use Figures 2 a cated expressions CO 3

3 30 Differentiate 3 y 4x2 3 2x 5 I 4 y 10x 7x 2 2x 5 y x e 7 f x 3x 5x e

Sketch the graph of the function by first making a table of values If an answer is undefined enter UNDEFINED f x x X 0 4 3 2 1 Sketch the graph f x x 17 y 20 20 y

Complete the table X 2 1 0 1 2 Sketch a graph of f f x x 3 720 x y

In Problems 1 4 use the definition f c lim AD f c h f c h to find the indicated derivative 1 f 1 if f x x 3 f 3 if f 1 1 5 s x 2x 1 7 r x 3x 4 9 f x ax bx c 11 f x x 2x 1 2 13 h x X 2 f 2 if f t 2x 4 f 4 if f s In Problems 5 22 use f x lim f x h f x h to find the derivative at x 6 f x ax 8 f x x x 1 10 f x x 12 g x x 1 14 S x

To graph the function f we plot the points x f x To graph f x x 3 we plot the following points x 2x x 0 x 1 x x 3 x x 3 So the point 4 in a coordinate plane is on the graph of f The height of the graph of f above the x axis when x 4 is

A graph of a piecewise defined function is given y 5 4 f x if x 2 3 5 4 3 2 1 1 2 2 if x 2 1 if 2 x 2 3 4 5 Find a formula for the function in the indicated form 1 2 3 4 x 5

In Problems 1 4 use the definition f c lim 0 to find the indicated derivative 1 f 1 if f x x 3 f 3 if f 1 2 1 In Problems 5 22 use f x the derivative at x 5 s x 2x 1 7 r x 3x 4 9 f x ax bx c 11 f x x 2x 1 13 h x IN f c h f c h X 2 f 2 if f t 2x 4 f 4 if f s lim x h f x h to find 6 f x ax B 8 f x x x 1 10 f x x 12 g x x x 14 S x X 1

3 12 pts Graph the following piecewise defined function Also what are the domain and range of this function f x x if 3 x 1 x if 1 x 4

4 12 pts A graph of a piecewise defined function is shown Find a formula for its function rule and also describe the domain and range of this function S 3 2 5 12 5 S X

2 12 pts Describe the domain of function g using set builder and interval notation g t 4 11 3t 8t 2t 15

the functions below to answer a through e f x 3x 5 a f g x a 3x 5 27 10 2x 3x 15 d gof x g x 2x 10 b h g x 9 3x 5 2 2x 5 2 0 2 2 4X 30X 25 10 e foh x h x 5x 3 c h f x 3X 5 5X 3 3x 5 5X 3 2x 8 b

Verify if the functions are inverses Show using function composition fog x x and gof x x f x 3x 2 g x 2 a fog x b gof x

A company manufactures and sells shirts The daily profit the company makes depends on how many shirts they sell The profit in dollars when the company sells a shirts can be found using the function f x 10x 40 Find and interpret the given function values and determine an appropriate domain for the function

Akilah flies a drone in a circular path around an object that is 240 meters north and 180 meters west of her position The drone s path takes it over a point that is 250 meters west and 190 meters south of her Find an equation for the drone s path Assume Akilah is located at the origin with the horizontal axis running east west and the vertical axis running north south The drone s path follows the equation

In June 2000 in the US there were 9135 wildfires that burned a total of 606 869 acres Convert these numbers to a unit rate of acres per fire Round your answer to the nearest tenth one decimal space

Find the domain of the functions 1 f x x 1 2 f x 5 x x 3 5 4 0 0 5 4 10 8 15 12

For any continuous piecewise linear function F on the interval a b we have x so F b F a x b a What is the relationship between x and the slopes of the lines on F on the interval a b Describe with examples and great detail