Calculus Questions

39 42 Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval 39 x x3 0 1 2 40 x 1 x 0 1 41 cos x x 0 1 42 sin x x x 1 2

etermine the largest open interval s of the domain over hich the function shown in the graph below is increasing b decreasing and c constant Then ve the d domain and e range a Over what open interval s if any is the function increasing Select the correct choice below and if necessary fill in the answer box complete your choice A The function is increasing on the open interval s Type your answer in interval notation Use a comma to separate answers as needed B The function is never increasing b Over what open interval s if any is the function decreasing Select the correct choice below and if necessary fill in the answer box t complete your choice A The function is decreasing on the open interval s Type your answer in interval notation Use a comma to separate answers as needed B The function is never decreasing

C Through 0 4 parallel to 5x y 9 C y Simplify your answer Use integers or fractions for any numbers in the expression

K Find the equation of the line that passes through the origin perpendicular to 3x y 7 Write the equation in slope intercept form The equation is y Simplify your answer Use integers or fractions for any numbers in the equation Do not factor

A person is driving a car on a straight road The graph shows the distance y in miles that the individual is from home after x hours Find the slope intercept form of the line y 0x 0 COP DLSLAACG LELO Ay 160 m 80 0 0 1 50 2 3 120 OU Time in hours

Through 6 7 perpendicular to 6x y 4 O The equation of the line is y Simplify your answer Type your answer in slope intercept form Use integers or fractions for any numbers in the expression

Write the slope intercept form of the line that passes through the given point with slope m Do not use a calculator Through 6 8 m 5 The equation of the line is y Simplify your answer Type your answer in slope intercept form Use integers or fractions for any numbers in the expression

K Find the slope intercept form of the equation of the line satisfying the given conditions Do not use a calcul Through 5 25 and 0 5 The slope intercept form of the line is y Simplify your answer Use integers or fractions for any numbers in the equation Do not factor

spe if defined of the line that passes through the given points 4 9 and 0 11 Find the slope of the line Select the correct choice below and fill in the answer box if necessary Type an integer or a fraction OA The slope of the line is B The slope is undefined

An initial investment amount P an annual interest rate r and a time t are given Find the future value of the investment when interest is compounded a annually b monthly c daily continuously Then find e the doubling time T for the given interest rate P 1500 r 2 95 t 8 yr a The future value of the investment when interest is compounded annually is Type an integer or a decimal Round to the nearest cent as needed b The future value of the investment when interest is compounded monthly is Type an integer or a decimal Round to the nearest cent as needed c The future value of the investment when interest is compounded daily is Type an integer or a decimal Round to the nearest cent as needed d The future value of the investment when interest is compounded continuously is Type an integer or a decimal Round to the nearest cent as needed e Find the doubling time for the given interest rate T yr C

K The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write a formula for f c Estimate the zero of f a The slope of the line is Type an integer or a simplified fraction CL

y 3x 6 Which of the following graphs does the equation most closely resemble OA Q OB Q G OC Q OD

For the linear function f x f 4 a f 2 1 Type an integer or a simplified fraction DA 4 a evaluate f 2 and f 4 b find the zero of f and c graph f How can the graph of f be used to determine the zero of f 1 2 Type an integer or a simplified fraction b The zero of f is 2 Type an integer or a simplified fraction c Choose the correct graph below A Q OB A Q Q G How can the graph of f be used to determine the zero of f OA Determine the zero of f by finding the x coordinate of the paint where the line intersects the x axis OB Determine the zero of f by finding the y coordinate of the point where the line intersects the y axis OC Determine the zero of f by finding the x coordinate of the point where the line intersects the y axis O D Determine the zero of f by finding the y coordinate of the point where the line intersesits the x axis DU OD Q

Select the correct choice below and fill in the answer box OA The equation of the line is OB The equation of the line is y

Graph the following line Also give the a x intercept if any b y intercept if any c domain d range and e slope of the line if defined Do not use a calculator X 5 a Find the x intercept Select the correct choice below and if necessary fill in the answer box to complete your choice A The x intercept is 5 0 Type an ordered pair using integers or decimals OB There is no x intercept C b Find the y intercept Select the correct choice below and if necessary fill in the answer box to complete your choice A The y intercept is Type an ordered pair using integers or decimals B There is no y intercept c Find the domain Select the correct choice below and fill in the answer box to complete your choice OA The domain is Type your answer in interval notation OB The domain is Type an integer or a decimal Use a comma to separate answers as needed Ay

Graph the following linear function Give the a x intercept b y intercept c domain d range and e slope of the line Do not use a calculator f x x 9 c Find the domain of the function Select the correct choice below and fill in the answer box to complete your choice A The domain is 00 00 Type your answer in interval notation The domain is Type an integer or a decimal Use a comma to separate answers as needed d Find the range of the function Select the correct choice below and fill in the answer box to complete your choice OA The range is Type an integer or a decimal Use a comma to separate answers as needed B The range is 00 00 Type your answer in interval notation e Find the slope of the line f x x 9 Select the correct choice below and if necessary fill in the answer box to complete your choice A The slope of the line f x x 9 is OB The slope is undefined

A particular country s exports of goods are increasing exponentially The value of the exports t years after 2007 can be approximated by V t 1 4e0 043t where t 0 corresponds to 2007 and V billions of dollars a Estimate the value of the country s exports in 2007 and 2020 b What is the doubling time for the value of the country s exports a The value of the country s exports in 2007 is billion Simplify your answer Round to the nearest tenth as needed Do not include the symbol in your answer The value of the country s exports in 2020 is billion Simplify your answer Round to the nearest tenth as needed Do not include the symbol in your answer b The doubling time is approximately years Simplify your answer Round to the nearest integer as needed

f x 7 what is the domain of f x 6 Given f x 2x 3 x 3 2 x 3 x 3 If f x x and gax x 2 5 what x y point did 0 0 become on If fl2 3 then f 3 f x x 7 find f x Graph f x 3 x 1 x X 2 X 3 10 Find fl4 Find f 3 The graph of g x contams the point a what is the corresponding point b what is the corresponding point 2 1 x 3 on glx glx If 31 is on the graph of f x what g x if glx f x 4 quint

Determine the domain and range of the relation and tell whether the relation is a function COLLE Using interval notation the domain is 4 4 Simplify your answers Type your answer in interval notation Using interval notation the range is Simplify your answers Type your answer in interval notation

Decide whether the relation to the right defines a function and give the domain and range Does the relation define a function Yos No What is the domain 2 3 4 Use a comma to separate answers as needed What is the range Use a comma to separate answers as needed CD

Use the graph of y f x to find each function value b f 0 a f 3 c f 5 d f 6 a f 3 0 b f 0

Decide whether the relation defined by the grap and range Does the graphed relation define a function No Yes What is the domain of the graphed relation 0 00 Type your answer in interval notation What is the range of the graphed relation Type your answer in interval notation

Exploration 2 1 13 Use Taylor s Theorem to derive the error terms the formulas and xo f xo f xo h f xo h 9 f xo h f xo h 2h error error h 2 f E h

Evaluate the integral sin x dx C 3

Jsi sin 6x cos xdx

Evaluate the integral 59 sec 460 de

Evaluate the integral S tan 11x sec 11x dx Stan 11x00 111

K Find f x at the indicated value of x f x 3 x 8 1 8

Use the graph of y f x to find each function value a f 3 c 1 5 a 1 3 b f 0 d f 6 Ay

K Evaluate the function f x 2x 8 at the indicated values a Find 1 3 b Find f 7 a f 3 Simplify your answer

Does the relation define a function Yes No What is the domain Use a comma to separate answers as needed

Decide whether the relation defined by the graph to the right defines a function and give and range Does the graphed relation define a function No Yes What is the domain of the graphed relation Type your answer in interval notation S

Write the set x 1 x 5 using interval notation and then graph the set on a number line The interval notation for the set x 1 x 5 is

Find the limit of the rational function a as x o and b as x co Write co or co where appropriate f x 3 x 3 a lim x 3 3 X X 5 b lim X 5 x x 3 3 YmX 5 11 Simplify your answer Simplify your answer

Find the equations of any vertical asymptotes for the function below x2 5x f x 3 x 36x Determine the equation of any vertical asymptotes Select the correct choice below and if necessary fill in the answer box within your choice OA The vertical asymptote s is are x Simplify your answer Use a comma to separate answers as needed OB There are no vertical asymptotes

Express the integrand as a sum of partial fractions Select the correct choice below and fill in any answer boxes to complete your choice Use integers or fractions for any numbers in the expression A OB U S X 4 2 x 9x 10 X 4 x 9x 10 S dx X 4 x 9x 10 Evaluate the integral x 4 x 9x 10 dx dx dx S S S 6 11 x 10 X 4 X 4 2 x 10 5 11 X 1 Ws dx dx 2 X 1 dx

Expand the quotient by partial fractions 6 x 14x 48 2 x 6 2 x 14x 48 Simplify your answer 3 X 8 I 3 X 6

The data show the number of felony convictions in hundreds and the crime rate in crimes per 100 000 for seven randomly selected states For the given data a determine the correlation coefficient between the number of felony convictions and the crime rate b find the equation of the regression line and c approximate what crime rate can we anticipate in a state that has 12 hundred felony convictions Felony convictions 114 110 7 109 3 106 105 104 9 Crime rate 102 99 5 100 4 99 94 2 103 95 5 93 3 OA a r 0 906 b y 14 11x 0 777 c 170 1 OB a r 0 906 b y 0 777x 14 11 c 4 8 O C a r 0 906 b y 0 777x 14 11 c 4 8

Express the integrand as a sum of partial fractions and evaluate the integral OB X 4 x 9x 10 O C Express the integrand as a sum of partial fractions Select the correct choice below and fill in any answer boxes to complete your choice Use integers or fractions for any numbers in the expression O A X 4 x 9x 10 S dx S x 4 SZ dx x 9x 10 X 4 dx x 9x 10 S dx S W x 10 X 1 X 4 X 4 x 10 dx dx 2 X dx

Computer the correlation coefficient rounded to the nearest thousandth for the following data y 3 13 A 0 905 OB 0 750 OC 0 905 OD 0 750 2 1 19 12 15 7 0 18

Perform long division on the integrand write the proper fraction as a sum of partial fractions and then evaluate the integral 12x 24x 1 2x 12x 12x 24x 1 2x dx dx

The accompanying data represent the percentages of teenagers in various countries that have used certain drugs Complete parts a through c below J K D B C D 40 5 20 1 E F G 37 19 22 16 H 1 5 6 4 52 35 3 17 7 14 4 31 23 Country Drug 1 x Other Drugs y A 22 5 a Determine the correlation coefficient between the percentage of teenagers who have used Drug 1 and the percentage who have used other drugs r Round to two decimal places as needed b Find the equation of the regression line for the percentage of teenagers who have used Drug 1 and the percentage who have used other drugs y x Round to two decimal places as needed c What percentage of teenagers can be anticipated to use drugs other than Drug 1 in a country where 10 of teenagers have used Drug 1 Round to the nearest whole number as needed

and 12 6 5 section Is the given ordered pair a solution to the system 6 4 3x y 22 2x 3y 24 O Yes No

Score 7 86 12 9 12 answered Question 11 Below one description one graph and one equation are equivalent Choose the proper set 10 9 8 7 You start with 3 Xbox360 games and each month you buy 2 new games You start with 1 Xbox360 games and each month you buy 3 new games Oy 3x 1 Oy 2x 3 do 10 9 8 7 5 2 3 4 6 7 8 9 p

Question 8 Terry is skiing down a steep hill Terry s elevation E t in feet after t seconds is given by E t 3700 40t The equation tells us that Terry started Select an answer Select an answer and his Select an answer is Select an answer by Select an answer Question Help Moc

Score 3 12 3 12 answered Question 9 If f x is a linear function f 5 5 and f 2 f x Question Help Video Message instructor 1 4 find an equation for f x

Question 10 A clothing business finds there is a linear relationship between the number of shirts n it can sell and the price p it can charge per shirt In particular historical data shows that 3000 shirts can be sold at a price of 35 while 10000 shirts can be sold at a price of 14 Give a linear equation in the form p mn b that gives the price p they can charge for n shirts Answer p Round the value of your slope to three decimal places Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer Question Help Video Message instructor Submit Question

Question 9 2 2 19 Part 1 of 6 Find the exact values of the six trigonometic functions for the following angle 45 HW O sin 45 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all dem

B 50 Need Help Submit Answer 0 06 0 12 Points X T X Read it Watch It DETAILS MY NOTES ASK YOUR TEACHER A graphing calculator is recommended Let f x 4e cos x a Find f x and f x PREVIOUS ANSWERS SCALCET9 3 3 034 PRACTICE ANOTHER

Differentiate y 8x 5 tan x