Calculus Questions

Graph f x 5x 1 1 First drag the two blue points on graph to the correct points that f x passes through Then use the remaining red point to drag the horizontal asymptote to the correct line Note that all three points are adjusted in increments of 1 4 Y

For the exponential function f x 6 5 1 find f 6 f 6 24300000

Evaluate the exponential function h x 4 for h 3 Round to 4 decimal places if necessary 3 help formulas h 3

The graph of f x 4 is shown below in blue This graph in red is a transformation of f x Write a function that describes the transformed function g x 6 2 0 f x g x

9 3 Problem 4 1 point Use the limit comparison test to determine whether diverges an lim n 00 bn a Choose a series n 19 your answer as a fully simplified fraction For n 19 72 19 lim 1 400 an lim 100 tr bn with terms of the form b an 71 19 8n 2n 19 2 3n4 converges or 1 and apply the limit comparison test Write np b Evaluate the limit in the previous part Enter o as infinity and o as infinity If the limit does not exist enter DNE Note You can earn 40 partial credit for 2 3 correct answers c By the limit comparison test does the series converge diverge or is the test inconclusive Choose

1 point Use the Integral Test to determine whether the infinite series is convergent n n 10 n 9 To perform the integral test one should calculate the improper integral dr Enter inf for inf for oo and DNE if the limit does not exist By the Integral Test the infinite series OA converges OB diverges n n 10 n 9

10 points Use the intermediate value theorem and the bisection method to approximate the real zero in the indicated in You only need to approximate to one decimal place f x 72 2x 5x 1 on 0 1

9 3 Problem 1 point The three series An Bn and Cn have terms 1 7210 C 2 3 Use the Limit Comparison Test to compare the following series to any of the above series For each of the series below you must enter two letters The first is the letter A B or C of the series above that it can be legally compared to with the Limit Comparison Test The second is C if the given series converges or D if it diverges So for instance if you believe the series converges and can be compared with series C above you would enter CC or if you believe it diverges and can be compared with series A you would enter AD n 1 5n5 n10 1309n15 9n5 5 5n 8n An 5n10 9n3 5 8n n 8n 9n 135n12 7 B 1 7257 C 1 1 n Hote To get full credit all answers must be correct Having all but one correct is worth 50 Two or more correct answers gives a score of 0

olve the following formula for the specified variable 1 2 gn m In gn cn for c O

Follow the steps for graphing a rational function to graph the function P x x x 6 36 Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer or once OC The graph will cross the x axis at x Type an integer or a simplified fraction Use a comma to separate answers as needed Type each answer on once D There is no x intercept Determine the vertical asymptote s if one exists Select the correct choice below and if necessary fill in the answe box es to complete your choice OA The function has one vertical asymptote Type an equation Use integers or fractions for any numbers in the equation B The function has two vertical asymptotes The leftmost asymptote is Type equations Use integers or fractions for any numbers in the equations and the rightmost asymptote is the middle asymptote is OC The function has three vertical asymptotes The leftmost asymptote is rightmost asymptote is Type equations Use integers or fractions for any numbers in the equations D The function has no vertical asymptote anc

Suppose an and bn are series with positive terms and bn is known to be divergent If an bn for all what can you say about an O A an diverges by Comparison Test OB an converges by Comparison Test C We cannot say anything about an

Follow the steps for graphing a rational function to graph the function R x 5x 5 8x 32 Write R x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice OA R x www Simplify your answer B R x is already in lowest terms Locate the intercept s of the graph Select the correct choice below and if necessary fill in the answer box es to complete your choice O A The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once B The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither x intercepts nor y intercepts 11

In each part find a formula for the general term of the sequence starting with 72 1 Enter the following information for an a an b an C d 11 5 1 1 1 3 9 27 1 1 9 27 2 8 26 80 3 9 27 81 0

Write the general formula for following alternating series in the form an 10 10 5 6 1 10 10 7 00

Write P x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice OA P x Simplify your answer B P x is already in lowest terms 36 Locate the intercept s of the graph Select the correct choice below and if necessary fill in the answer box es to complete your choice OA The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once and no x intercept OC The graph has y intercept Simplify your answer Type an integer or a fraction D The graph has neither x intercepts nor y intercepts

2 Evaluate the indicated limits If it does not exist is the limit or neither lim x 2x x 2x b lim x 6x x I 118 X48 a X x 2 2x c lim d lim x118 4 3x x6 9

Follow the steps for graphing a rational function to graph the function G x OD The domain is the set of all real numbers Write G x in lowest terms Select the correct choice below and if necessary fill in the answer box within your choice OA G x Simplify your answer B G x is in lowest terms X ZA 4 Find the intercepts of the graph Select the correct choice below and if necessary fill in the answer box es within your choice OA The graph has x intercept s and y intercept Simplify your answers Type integers or fractions Use a comma to separate answers as needed Type each answer only once OB The graph has y intercept and no x intercept Simplify your answer Type an integer or a fraction OC The graph has x intercept s and no y intercept Simplify your answer Type an integer or a fraction Use a comma to separate answers as needed Type each answer only once OD The graph has neither x intercepts nor y intercepts

Solve the inequality algebraically x 7 x 9 X 0 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numb expression

15 A 4v 17 2v 4m 4nm 1 B 42 D 2v 3 18 2x A 4x C x 18 2u y 3 2u A B B 3 x 2 1 2

Follow the steps for graphing a rational function to graph the function P x X X 0 x 6 x 6 B P x cannot be factored further A P x Type your answer in factored form Do not simplify X X 6 36 What is the domain of P x Select the correct choice below and if necessary fill in the answer box to complete your choice OA xx B xlx C x x 6 6 Type an integer or a simplified fraction Use a comma to separate answers as needed OD The domain is the set of all real numbers Type an integer or a simplified fraction Type an integer or a simplified fraction OA P x Simplify your answer OB P x is already in lowest terms Write P x in lowest terms Select the correct choice below and if necessary fill in the answer box to complete your choice

Solve the inequality f x 0 where f x x 1 x 2 by using the graph of the function 4 2 30 20 10 10 20 30 40 50 2 4 X C The solution set for f x 0 is Type your answer in interval notation

Solve the inequality algebraically X 3 X 6 0 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numbe expression

Solve the following inequality x 2 x 3 x 6 0

2 x 64x What is the solution Type your answer in interval notation Simplify your answer Use integers or fractions fo expression

Decide whether the following statement is true or false The graph of f x x x 0 or x 2 X is above the x axis for x 0 or x 2 so the solution set of the inequality X 2 Choose the correct answer below True False ww X x 2 20 is

X Follow the steps for graphing a rational function to graph the function G x 4 If needed first write the given function as a single rational expression Then factor the numerator and denominator of G x Select the correct choice below and if necessary fill in the answer box within your choice 1x x 2 x 2 OB G x cannot be factored further What is the domain of G x Select the correct choice below and if necessary fill in the answer box within your choice Type an integer or a simplified fraction A G x Type your answer in factored form Do not simplify OA xx OB xx Type an integer or a simplified fraction Use a comma to separate answers as needed OC x x Type an integer or a simplified fraction OD The domain is the set of all real numbers

low the steps for graphing a rational function to graph the function R x x 2x 63 x 4x 21 X

Follow the steps for graphing a rational function to graph the function R x ww 5x 5 8x 32 If needed first write the given function as a single rational expression Then factor the numerator and denominator of R x Select the correct choice below and if necessary fill in the answer box to complete your choice A R x 5 x 1 8 x 4 OB R x cannot be factored further What is the domain of R x Select the correct choice below and if necessary fill in the answer box to complete your choice Type your answer in factored form Do not simplify OA X X Type an integer or a simplified fraction Use a comma to separate answers as needed OB x x 2 Type an integer or a simplified fraction OC xx Type an integer or a simplified fraction OD The domain is the set of all real numbers

3 Evaluate the following limits cos x a lim sin x 0 COS X X 1 3 1 x1 x 1 b lim

Use Newton s method with the specified initial approximation x to find x3 the third approximation to the root of the given equation Round your answer to four decimal places x5 x 7 0 x 1 X X3 3 2677

24 25 Find the magnitude of the resultant force and the angle it makes with the positive x axis 24 YA 0 45 30 20 lb 16 lb X 25 till hirido su 300 N YA 0 1 200 N 60 XOX

37 If r x y z and ro points x y z such that r ro 1 xo yo Zo describe the set of all

17 Find a unit vector with the same direction as 8i j 4k

33 The region consisting of all points between but not on the par spheres of radius r and R centered at the origin where r R

21 30 Describe in words the region of R represented by the ning sill equations or inequalities 21 x 5 23 y 8 22 y 2 24 x 3

13 16 Show that the equation represents a sphere and find its center and radius 13 x y 2 2x 4y 8z 15

Finding antiderivatives Use what you know about derivatives to finc all antiderivatives of the following functions Sum Rule a f x 3x f x g x 2 1 b f x 2 1 x c f x sin x

2 8 points Using transformations sketch the graph of y f x 1 3 labeling all points Plea place your final answer to the right the other graphs below are for intermediate one if needed FINAL ANSWER 4 0 2 4 3 y f x 0 0 4 0 1 2 3 4 5 2 2 12345 3

Find an arc length parametrization of the line y 72 12 Use symbolic notation and fractions where needed Give your answer in the form of comma separated list of 1 j components Fi 9 a help fractions

99 Suppose 7 a 6 3 2 b 8 c 16 d 2 2 e 6 3 2 12 7 4 and and let g x f x cosx Find TU

36 Find the derivative of the function using the definition of derivative f x 5x 2 4x 3

6 The slope of the tangent line to the graph of the exponential function y 9 at the point 0 1 is lim 9x Estimate the slope to three decimal places X 0 a 2 485 b 2 303 c 2 565 d 2 197 e 2 079 X

work No credit for digital work 1 6 points Assume f x dx 3 f f x dx 5 and f3 g x dx 9 compute 3 3

A car was valued at 38 000 in the will it be worth by 2017 year 2007 By 2013 the value had depreciated to 11 000 If the car s value continues to drop by the same percentage w help numbers

Provide a detailed sketch with analysis of the function f x x on the domain 0 Your sketch must include the following details all of which must be justified any local and any global extrema of f limo f x limx f x concavity of f

The fox population in a certain region has an annual growth rate of 4 per year In the year 2012 there were 27790 foxes counted in the are Write a function f t that models the number of foxes in the population at t years after 2012 Assume a continuous growth rate f t help formulas What is the fox population predicted to be in 2020 help numbers

9 Determine whether the points lie on a straight line a A 2 4 2 B 3 7 2 C 1 3 3

3 Compute lim x arctanx 1 x T 2 Justify your answer

3 Which of the points A 4 0 1 B 3 1 5 and C 2 4 6 is closest to the yz plane Which point lies in the xz plane

130t 7t 100 Click here to access the Desmos Graphing Calculator and use it to approximate the time when the concentration is highest help numbers The concentration C of a drug in a patient s bloodstream t hours after injection is given by C t t GI