Calculus Questions

3 Use the nth Term Test for divergence to show that the series is divergent or state that the test is inconclusive a 1 b ln n 1 n 8 n 1 n 2 n 3

2 Write out the first 5 terms of the sequence with its first term along with the recursion formula for the remaining terms a 2 an 1 na n 1

Does the sequence an converge or diverge Find the limit if the sequence is convergent an In n 6 n Select the correct choice below and if necessary fill in the answer box to complete the choice OA The sequence converges to lim an n1x OB The sequence diverges Simplify your answer

Use the formula for the nth term a of a sequence a Find the values of a a2 a3 a4 1 a

Use a calculator in radian mode to find an approximate value of the expression correct to five decimal places if it is defined If an answer is undefined enter UNDEFINED sin 0 25718 534 90280

Does the sequence a converge or diverge Find the limit if the sequence is convergent an 1 2 Select the correct choice below and if necessary fill in the answer box to complete the choice O A The sequence converges to lim an 81x Type an exact answer OB The sequence diverges

Use a efinite integral to find the area under the curve between the given x values f x 3x 6x 3 from x 1 to x 2 square units

Use a definite integral to find the area under the curve f x 6 x from x 0 to x 6 square units Make a sketch of the curve showing the region y 2 95 y 6 2 N y 6 2 y 6 2 6

2 3 2 Sin 5 7 Fo 3

n 0 To cos 0 1

A cost function is given by C x 5 2x 100 6 What is the correct form for the marginal cost Hint You may want to make use of the fact that d ax b an ax b 1 dx Select the correct answer below O MC 60 2x 100 5 O MC 30 2x 100 5 O MC 30 2x 100 5 OMC 60 2x 100 5

Cooper Section 3 2 52 On the planet Golgafrincham there are two systems for measuring temperature Using the Celia scale water freezes at 0 C and boils at 50 C Using the Furryhat scale water freezes at 10 F and boils at 110 F Both systems divide the temperatures in between into equal increments Letz be the temperature in degrees Celia and y be the temperature in degrees Furryhat a Find a formula which converts temperatures measured in Celia into Furryhat y x 9 5 F b Find a formula which does the inverse x y c What temperature is the same in both Celia and Furryhat C

Graph several level curves of the following function y Draw the level curves for z 1 z 2 z 3 and z 4 Choose the correct graph below OA OB OC ROO Q 5 Q OOS 27 O OU OD

2 Refer to the function below to do the problems that follow Do not use a calculator That is for each problem be sure to show your work or justify your answer f x x 2x15 2x 3 a State the domain Use interval notation 4 points b Give the equation of each VERTICAL asymptote 4 points

1 Refer to the graph below to do the problems that follow 10 6 6 8 10 a State the domain of the function whose graph is shown Use interval notation 4 points b Give the equation of each VERTICAL asymptote 4 points c Give the equation of the HORIZONTAL asymptote

Consider the cost function C x 1x where x is the number of product units If the marginal cost at x 400 units is 100 what is the value of a C x 1 000 ax

c 4 509 793 511 est proche de d 7 108 991 868 est proche de 4 a Estime la valeur de 1 104 886 Je peux arrondir chaque nombre au millier le plus proche 1104 1000 09 886 1000 1 000 1 000 1 104 886 est proche de Effectue l addition pour v rif le r sultat est proche de ton b Estime la valeur de 2 804 12117 O

1 Given a function of g x 10 3x 5 answer the following questions 2 points each A Find the slope of the line tangent to the graph of g x at 0 2 B Determine an equation of the tangent line at 0 2

3 Given an equation coty 4x 0 5y x use implicit differentiation to find dy a

Find the derivative of w x 1 x 6x 4x x 1

Given a graph shown to the right answer the following questions A Find the values of x in 0 4 where g x is discontinuous 2 points B Find the values of x in 0 4 where g x is indifferentiable 2 points C Draw g x on the graph below 2 points the den Moed 13 16 g x 1 1 0 1 2 3 YA 4 3 2 1 0 A 2 y g x 2 173 3 4

39 Given y f x x In x find dy dx

Find the derivatives of the following functions 2 points each Deniwalotarll A f t 10 t 500 t 1000 79 5x 1 3 nex

tan x cotr 1 6 Given y f x find dy dx

The function graphed below is defined by a polynomial expression of degree 4 Use the graph to solve the exercise YA M a If f is increasing on an interval then the y values of the points on the graph rise b Iff is decreasing on an interval then the y values of the points on the graph fall V as the x values increase From the graph of f we see that f is increasing on the intervals as the x values increase From the graph of f shown above we see that fis decreasing on the intervals x Enter your answer using interval notation X Enter your answer using interval notations

3 Cubmit Answer 0 se domain of the function is all the x aswers using interval notation Need Help Read It values of the points on the graph and the range is all the corresponding y values From the graph off we see that the domain of f is the interval 00 00 and the range of f is the interval 00 00 x Enter your

all 15 0 0 P bo Free Response Questions 7 Line is tangent to the graph of y x 7 the figure above b Write an equation for line a Find the x coordinates of point P 2018 R 9 To l x y x fe 120 K atea or at 3650 120 60 30 mih alf DIN of 10orpor am bab in2 ung ad to col foldi mo s die win at the point P and intersects x axis at 15 0 as shown in 120 If the line of symmetry for the curve v x x 60 37 120 0 line of symmetry olid goal solomatin y kx b toshod s and age aft et tu tolnimi neb siit zd foblev al snil basyas intersects line at point R what is the length of Ona

Let A be an invertible square matrix a What is the column space of A b What is the null space of A

Differentiate the function f x 2 0 f x Enter an integer or decimal number more

Show that the curve y 7x 7x 2 has no tangent line with slope 1 y 7x 7x 2 m y for all x Question Help Message instructor but Select an answer 0 for all so m

Find d106 da 106 sin x

Find the first and second derivative of the function G r T T G r G r

Find the first and second derivatives of the following function f x 9x 3x 6x x f x

Ques Find an equation of the tangent line to the curve at the given point y 3x x 1 2 y Illustrate by graphing the curve and the tangent line on the same screen O 5 13 2 1 8 6 4 2

C Differentiate the function R a 5a 1 R a

Differentiate the function 3 F x F x 5 I 10

Differentiate f x 428 5 cos x f x

Differentiate the function S R 8TR S R

Differentiate the function B y cy 6 B y

Differentiate the function h x x 2 3x 4 h x

You would like to have 3500 in 5 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 4 comp parts a and b Click the icon to view some finance formulas a How much should you deposit at the end of every six months In order to have 3500 in 5 years you should deposit at the end of every six months Do not round until the final answer Then round up to the nearest dollar More info In the provided formulas P is the deposit made at the end of each compounding period for an annuity that pays an annual interest rate r in decimal form compounded n times per year and A is the value of the annuity after t years A P 1 1 n P A 2 M n X

ose that you earned a bachelor s degree and now you re teaching high school The school ct offers teachers the opportunity to take a year off to earn a master s degree To achieve goal you deposit 5000 at the end of each year in an annuity that pays 6 compounded Jally How much will you have saved at the end of five years Find the interest Click the icon to view some finance formulas Formulas In the following formulas P is the deposit made at the end of each compounding period r is the annual interest rate of the annuity in decimal form n is the number of compounding periods per year and A is the value of the annuity after t years 371 A P 1 r 1 r A P a After 5 years you will have approximately Do not round until the final answer Then round to the nearest dollar as need nt In the following formulas P is the principal amount deposited into an account ris the annual interest rate in decimal form n is the number of compounding periods per year and A is the future value of the account after t years 0 P 1 r A P 1 X

he given X 7 X 49 f x Tipiones Use integers or tractions for any numbers in the equations OC There are no vertical asymptotes Find the horizontal or oblique asymptotes Select the correct choice below and if necessary fill in the answer box to complete your choice A The equation of the oblique asymptote is Use integers or fractions for any numbers in the equation B The equation of the horizontal asymptote is y 0 Use integers or fractions for any numbers in the equation OC There are no horizontal or oblique asymptotes Find the coordinates of any holes in its graph Select the correct choice below and if necessary fill in the answer box to complete your choice OA There is a hole in the graph off at the point Type an ordered pair using integers or fractions B There is no hole in the graph of t

a Find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following 1 4 to 5 ii 4 to 4 5 iii 4 to 4 1 b Find the instantaneous rate of change when r 4 A 4

Give the equations of any vertical horizontal or oblique asymptotes for the graph of the rational function x2 5x 6 2x x 21 f x OA There is one vertical asymptote Its equation is Type an equation Use integers or fractions for any numbers in the equation B There are two vertical asymptotes The equation of the leftmost one is x 3 and the equation of the 7 rightmost one is x 2 Type equations Use integers or fractions for any numbers in the equations OC There are no vertical asymptotes Identify the horizontal or oblique asymptote if one exists Select the correct choice below and if necessary fill in the answer box to complete your choice OA The horizontal asymptote is Type an equation Use integers or fractions for any numbers in the equation OB The oblique asymptote is Type an equation in slope intercept form Use integers or fractions for any numbers in the equation

K For the given function find all asymptotes and the coordinates of any holes in its graph 3x 1 f x 5x 12x 9 OA There is one vertical asymptote Its equation is Use integers or fractions for any numbers in the equation B There are two vertical asymptotes The equation of the leftmost one is x 3 and the equation of the 3 rightmost one is x 5 Use integers or fractions for any numbers in the equations OC There are no vertical asymptotes Find the horizontal or oblique asymptotes Select the correct choice below and if necessary fill in the answer box to complete your choice OA The equation of the oblique asymptote is Use integers or fractions for any numbers in the equation OB The equation of the horizontal asymptote is Use integers or fractions for any numbers in the equation 5

For the given function find all asymptotes and the coordinates of any holes in its graph f x X 7 x 49 complete your choice A There is one vertical asymptote Its equation is x 7 Use integers or fractions for any numbers in the equation OB There are two vertical asymptotes The equation of the leftmost one is rightmost one is Use integers or fractions for any numbers in the equations OC There are no vertical asymptotes OA The equation of the oblique asymptote is Find the horizontal or oblique asymptotes Select the correct choice below and if necessary fill in the answer box to complete your choice Use integers or fractions for any numbers in the equation OB The equation of the horizontal asymptote is and the equation of the Use integers or fractions for any numbers in the equation C There are no horizontal or oblique asymptotes

domain of f f x 1 5x 3x 3 complete your choice A There is one vertical asymptote Its equation is x 1 Type an equation Use integers or fractions for any numbers in the equation B There are two vertical asymptotes The equation of the leftmost one is rightmost one is Type equations Use integers or fractions for any numbers in the equations OC There are no vertical asymptotes and the equation of the Identify the horizontal or oblique asymptote if one exists Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function has a horizontal asymptote whose equation is Type an equation Use integers or fractions for any numbers in the equation OB The function has an oblique asymptote whose equation is Type an equation in slope intercept form Use integers or fractions for any numbers in the equation C The function has neither a horizontal nor an oblique asymptote

Suppose that a population of bacteria triples every hour and starts with 500 bacteria Find an expression for the number n t Use it to estimate the rate of growth of the bacterial population at 1 5 hours Round your answer to the nearest whole number bacteria hr n 1 5

Graph the following rational function by hand Give the domain and range and discuss symmetry and any asymptotes f x 10x Choose the correct graph below OA OB The domain is Type your answer in interval notation OC G D Q 5