Calculus Questions

12 Find the quotient Q x and the remainder R x when g x x Find the sum of all the zeros of the polynomial function g x 4x 0

0 Which of the following numbers is not a potential zero of f x 18x 9x 5x 2 3 1 e 2 2 a 2 b 2 9 c 1 1 1 or to ante

13 Find the horizontal asymptote HA and vertical asymptote VA of x 4 f x x x 2 a HA y 1 b HA y 0 c HA y 1 d HA y 0 e HA None VA x 0 x 2 VA x 0 x 2 VA x 0 VA x 0 VA x 0 x

Find the horizontal asymptote s HA and the vertical asymptote s VA of the functia f x 3219 a HA lines y 3 and y 3 VA line x 0 b HA c HA line y 3 VA line x 0 d HA line 2 0 VA line y 3 e HA line y 0 VA line x 3 none VA lines 3 and x X 3

20 Identify the solution set of the quadratic inequality x 2x 3 0

Given that x a x 3 and x b x 3 and x 1 2 c x 3 and x 1 d x 3 and x 1 is a zero of f x 2x 5x 4x 3 find the other zeros of f x biton bus ancilsmot e r 3 and x 1 Rewrite the polynomial f x in completely factored form

Find the asymptotes of the function f x 2 x 4 x x 2

Let f x 2 x 3 Find 1

Find the vertical asymptotes VA of f x x 5x 6 x 9 a Lines x 2 and x 3 b Lines x 2 and x 3 c Line x 2 d Lines y 2 and y 3 e Lines y 1 Are they any holes Where

Which of the following functions is not one to one a f x x 2x on 1 00 b f x x x 1 on 0 0 c f x 2x 5 on 0 00 d f x x 4 on 0 00 e f x 2x 4 x on 00 00

Find the interval that represents the sotution set to the inequality x 1 3 x 4 Which of the following numbers is not a potential zero of f x 18x 9x 5x 2 3 c d e 2 a 2 b 2 2

7 8 Solve the inequality x26 x Express the solution set in interval notation Solve the inequality x x 2 1

If a function is one to one then could points 4 2 and 4 2 lie on the graph of the function and why If a function is even then could points 4 2 and 4 2 lie on the graph of the function and why If a function is even then could points 4 2 and 4 2 lie on the graph of the function and why If a function is odd then could points 4 2 and 4 2 lie on the graph of the function and why If a function is odd then could points 4 2 and 4 2 lie on the graph of the function and why

2 If x 2 is a zero of the polynomial function P x 11x 17x 6x3 2 find the sum of the other zeros of the polynomial

3 x Solve the inequality 3 Express the solution set in interval notation x 2

If function g x is odd and g 3 2 lies on the graph of the function what are the coordinates of the point that will also lie on the graph of the function If function g x is even and g 3 4 lies on the graph of the function what are the coordinates of the point that will also lie on the graph of the function

Solve the differential equation by the method of integrating factors dy dx y 2xy Use C to represent any constant of integration

Solve the initial value problem y 3y e y 0 0

Solve y 7x y x6 y 1 7 a Identify the integrating factor a z a x 0 b Find the general solution y x Note Use C for an arbitrary constant c Solve the initial value problem y 1 7 y x

46 lim x ln 1 8118 48 lim x3 2 sin 1 x 818

48 lim x3 2 sin 1 x

61 lim x 1 0 2 14 63 lim x

x 0 x4 43 lim x sin m x x18

29 lim x 0 tan x sin x 31 lim x 0 tanh x x 33 lim X x3 x 0 3

8 70 Find the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using it If l Hospital s Rule doesn t apply explain why X 3 8 lim x 3x 9 9 lim 11 lim x 1 x1 x 1 13 lim 15 lim 1 0 x 2x8 x 4 17 lim 19 lim sin x x 4 tan x 1 e2 1 sin t sin x 1 x1 x x 2 x x 1 e COS X x 8 x 2 x 2 10 lim 12 lim x 4 x 4 tan 3x x 0 sin 2x 14 lim x 2 x x 0 1 cos x 16 lim 1 cos 0 8 1 cos 0 18 lim 20 lim x x x 1 2x

If you choose to not do these problems please do not turn in the assignment 1 extra credit 10 pts Consider the function of two variables given by 1 f x y x y x yl Experiment with fon scratch paper for various real number inputs in place of 2 x and y Show two of the calculations below and briefly explain what this function does

If 380 000 of bonds are issued during the year and 130 000 of bonds are retired during the year the statement of cash flows indirect method will show a n Select one a net decrease in cash of 250 000 in the operating activities section b net increase in cash of 250 000 in the operating activities section c net gain on retirement of bonds of 250 000 in the financing activities section d increase in cash of 380 000 in the financing activities section and a decrease in cash of 130 000 in the financing activities section

Describe the graph of fit f 0 1 and f x 3 for x

2 20 pts Consider the quadratic function g x 2x 16x 29 a What is the y intercept of the function for yintercept put O y 2x0 16 Y0 29 29 b What are the x intercepts of the function If the function has no x intercepts say so but show your work c Use completing the square to write the function in standard form d List a sequence of transformations to get from the graph of y x to the graph of g Sketch a graph of y g x Does the graph open upward or downward Where does the global maximum or minimum value of the function occur What is this global maximum or minimum value Where is the function increasing and decreasing same 0772 mo m T fo Re

a Use definition 1 p 133 to find the slope of the line tangent to the graph off at P b Determine an equation of the tangent line at P c Plot the graph of f and the tangent line at P 15 f x x 5 P 3 4 16 f x 3x 5x 1 P 1 7 1 17 f x P 1 1 X 4 18 f x 2 P 1 4 19 f x 3x 3 P 2 3 720 f x P 4 1

28 F v a v 1 O

2 cos ma 1 1 1 z L Hopital Rule or Taylor series expansion 3 Evaluate lim 140 in terms of m where me R 0 You are not allowed to use 10 montiol

he velocity function is u t t2 3t 2 for a particle moving along a line Find the displacement and the distance traveled by the article during the time interval 3 6 isplacement istance traveled needed see page 287 of the Stewart Essential Calculus textbook for the definitions of these terms

tetan A sofa regularly sells for 430 The sale price is 382 70 Find the percent decrease of the sale price from the regular price

Current Attempt in Given the demand curve p 132 q and the supply curve p 4 q2 find the producer surplus when the market is in equilibrium Round your answer to 3 decimal places The producer surplus is i when the market is in equilibrium

A desalination process reduces the amount of salt in a container of water by 4 per hour If 35 grams is the initial amount o alt then the amount of salt remaining after r hours is modeled by S 35 x 0 96 grams Make a graph of the amount of salt remaining after 7 hours Suggestion You may zoom in to the graph to manage points easier Double click any point to view the coordinate the point i placed Round coordinates to one decimal place where needed

A sofa regularly sells for 510 The sale price is 397 80 Find the percent decrease of the sale price from the regular price

Consumers millions y 56 54 52 Potato Chips Consumption 5 55 35 50 48 46 44 42 0 42 97 40 0 1 2 3 4 5 6 7 8 9X Years Since 2011 FOOD The graph shows the number of people in the U S who consumed between 8 and 11 bags of potato chips in a year since 2011 a Use the graph to estimate the average rate of change of consumption from 2011 to 2016 Then check your results algebraically b Interpret your results in the context of the situation

Write the parametric equations as a function of a in Cartesian form S 1 with a 0 t x 3e y 6e 4

23 28 a Find the intervals on which f is increasing or decreasing b Find the local maximum and minimum values of f c Find the intervals of concavity and the inflection points 23 f x x 2x 3 24 f x X x 1

1 3 y y4 12 R t t e 3 t II F y 13 y X 1 x x y 5y 14 y X 1 x x

4 g x x ex

10 Y u u u u 2u

16 y 18 y t 1 1 S kes

Find the consumer surplus for the demand curve p 100 3q when q 5 units are sold at the equilibrium price The consumer surplus is 187 5 X

12 R t t e 3 t

8 f t 2t

3 f x x 2x ex 4 g x x e

7 g x 3x 1 2x 1 9 V x 2x 3 x 2x I0 Y u u 2 u 3 u 2u 8 f t 2t 4 t

Suppose that you earned a bachelor s degree and now you re teaching high school The school district offers teachers the opportunity to take a year off to earn a master s degree To achieve this goal you deposit 2000 at the end of each year in an annuity that pays 7 compounded annually a b How much will you have saved at the end of five years Find the interest Click the icon to view some finance formulas a After 5 years you will have approximately Do not round until the final answer Then round to the nearest dollar as needed