Calculus Questions

1 Three teams of scientists measured the time it takes a certain beam of particles to travel a given distance Here are their results reported in milliseconds ms in random order 9 11 5 Team A Team B Team C Team A Team B 15 Team C 3 17 5 11 5 10 Which team has the lowest standard deviation 9 11 15 All teams have the same standard deviation 15 9

Use the graph of the piecewise function y fx given above to answer questions 15 18 A 15 What is the domain of the function y f x A 4 4 B 2 6 C 16 What is the absolute maximum value of the function y f x A 3 17 Evaluate 0 A I B 4 C 4 0 U 0 4 B2 C 5 C 3 D 1 5 D 6 D nonexistent 18 What is the equation of the line segment of the piecewise function y f x from 0 x 4 A y x 3 B y x C y x y 1 x 1

IF F x x 1 ar x 3 4x then

The function f x 2x 33x 108x 5 has two critical numbers Use the derivative to algebraically find the critical numbers The smaller one equals and The larger one equals Hint Factor carefully

A 2 If f x 3 5x then f 1 A 8 B 2 C 2 D 8

Next question Find the following using the table below X 1 2 3 4 f x 1 3 2 4 f x 4 2 1 3 g x 2 3 1 4 g x 4 2 1 3 h 3 if h x f x g x 3 f x g x h 3 if h x Get a similar question 1 h 3 if h x f g x 4 OFF

Suppose that A Find an equation for the tangent line to the graph of fat x 2 Tangent line y f x 5x 2 B Find the average of all values of a where the tangent line is horizontal If there are no such values enter 1000 Average of a values

Find an equation of the tangent line to the curve at the point y Tangent line V y sin 5x cos 6x

0 26 1 04 Points Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f If an answer does not exist enter DNE 16 x2 3x 2 f x absolute maximum absolute minimum local maximum DETAILS local minimum 16 0 DNE PREVIOUS ANSWERS DNE if 4 x 0 if 0 x 4 X SCALCET9 4 XP 1 008 X Enhanced Feedback Please try again Use the first and second derivatives to find the intervals where the function is increasing or decreasing and where the function is concave up or down

Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE h t t3 4 gt 4 2 9 0 0 t 9 X Your Your answer cannot be understood or graded More Information

coth x sech x csch x Need Help Submit Answer Read It DETAILS 5 0 78 1 04 Points Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f Enter your answers as a comma separated list If an answer does not exist enter f x x 9x absolute maximum value absolute minimum value local maximum value s value s Watch It 8 if 1 x 0 if 0 x 1 1 DNE 0 PREVIOUS ANSWERS SCALCET9 4 1 027 X

If tanh x 3 sinh x cosh x 1 coth x 41 9 sech x 40 41 csch x 40 9 9 40 find the values of the other hyperbolic functions at x X X x X X

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f If a answer does not exist enter DNE f x absolute maximum local maximum J16 x 13x 2 absolute minimum local minimum if 4 x 0 if 0 x 4

If f 2 5 and f x 2 for 2 x 5 how small can f 5 possibly be f 5 2

a Send a survey home with every student and ask parents to fill it out and return it the next day Which kind of sampling strategy is involved This question 2 point s possible In a large city school system with 21 elementary schools the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade The PTA wants to find out whether parents agree with this plan Listed below are some of the ideas proposed for gathering data For parts a through d indicate what kind of sampling strategy is involved and what if any biases might result Assume the schools are homogeneous and differ from each other OA An attempt at a census OB Systematic sampling OC Convenience sampling OD A simple random sample What kind of bias if any is most likely to result OA Response bias could result since the PTA wants parents to agree to this plan OB Undercoverage bias could result since only parents involved with the PTA will be sampled Submit test

o refer to later to find your errors and correct them After the quiz due date you will be able to see hints the ebook link s tutorials and Practice Another Version for the problems on the quiz Be sure to review your answers and udge how well you understood the methods used This is the most mportant part of taking each quiz learning from your mistakes Good luck 1 1 04 Points DETAILS b cosh 0 SCALCET9 3 11 001 Find the numerical value of each expression a sinh 0

Suppose that 4 f x 5 for all values of x What are the minimum and maximum possible values of f 8 f 3 f 8 f 3

Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f Enter your answer as a comma separated list If an answer does not exist enter DNE f x x 8 9x absolute maximum value absolute minimum value local maximum value s local minimum value s if 1 x 0 if 0 x 1

Find the numerical value of each expression Round your answers to five decimal plac a tanh 0 b tanh 1

7 10 75 Points Verify the identity algebraically Use a graphing utility to check your result graphically 6 cot a 6 csc a 6 csc a 1 cot a DETAILS 6 cot a csc 1 Multiply the numerator and denominator by a common expression and then use a Pythagorean Identity to simplify Simplify your answers completely csc a 1 Need Help Submit Answer LARPRECALCRMRP7 5 2 058 6 cot a csc a 1 6 cot a csc a 1 Read It cot a 8 1 Points DETAILS Use the cofunction identities to evaluate the expression without the aid of a calculator MY NO LARPRECALCRMRP7 5 2 069 MI MY NOTES

A study examined brain size measured as pixels counted in a digitized magnetic resonance image MRI of a cross section of the brain and IQ 4 Performance scales of the Weschler IQ test for college students The scatterplot to the right shows the Performance IQ scores vs the brain size Describe the association between brain size and IQ as seen in the scatterplot Choose the correct answer below OA There is a very weak or possibly no association between the two variables OB There is a fairly strong positive straight association between the two variables OC There is a weak negative curved association between the two variables but there is at least one outlier OD There is a moderately weak negative curved association between the two variables OE There is a moderately weak positive straight association between the two variables Performance IQ 140 120 100 x xxxx 80 x X 825 X Submit test X x X 975 Brain Size pixels

Researchers have linked an increase in the incidence of lung cancer in Austria to a pollutant released by an industrial accident The study identified 995 people who lived near the site of the accident and were under age 40 at the time Seventeen of the people had developed lung cancer at an unusually young average age of 45 Medical records showed that they had heightened concentrations of the pollutant in their blood and that each tenfold increase in the level of the pollutant was associated with a doubling of the risk of lung cancer Complete parts a through e below a Identify whether the research is an observational study or an experiment The research is an b Identify whether i It is c Identify the subje observational study experiment elected Choose the correct answer below OA Austrian peop OB People exposed to the pollutant from the industrial accident OC The medical records of the people exposed to the pollutant mit test

Refer to the graph to the right and follow the directions in parts a through 1 a is a 1 or is 0 a 1 b Give the domain and range of f and the equation of the asymptote c Sketch the graph of g x a d Give the domain and range of g and the equation of the asymptote e Sketch the graph of h x a f Give the domain and range of h and the equation of the asymptote f x ax 1 5 1 a 0 1 a is a 1 or is U a 1 Choose the correct answer below A For the function f x a a 1 because as a gets closer to 0 the graph becomes steeper moving to the left of the y axis B For the function f x a a 1 because as a becomes larger the graph becomes steeper moving to the right of the y axis OC For the function f x a 0 a 1 because as a gets closer to 0 the graph becomes steeper moving to the left of the y axis b Give the domain and range of f and the equation of the asymptote The domain of fis OD For the function f x a 0 a 1 because as a becomes larger the graph becomes steeper moving to the right of the y axis

4 7 16 The solution set is Simplify your answer Type an integer or a fraction KEK

Determine whether the function is one to one If so a write an equation for the inverse function in the form y f x b graph f and on the same axes and c give the domain and the range of f and f If the function is not one to one say so The Uncon IS TRUL U 10 01 b Choose the correct graph for f and below The graph of f is shown in solid blue The graph of f is shown in dashed red OA Q L B OA The domain of fis Q c Give the domain and range of f and r Begin by finding the domain and range of f x Select the correct choice below and if necessary fill in any answer boxes to complete your choice and the range of fis Type your answers in interval notation B The function is not one to one D The function f x is not one to one

Select the correct choices that complete the sentence below If two functions f and g are inverses then fog x and g x f x

Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f Enter your answers as a comma separated list If an answer does not exist enter DNE T f x sin x 0 x absolute maximum value absolute minimum value local maximum value s local minimum value s Need Help Read It Du

The rate of change of the function fx 9 sec x 9 cos x is given by the expression 9 sec x tan x 9 sin x Show that this expression can also be written as 9 sin x tan x Use the Reciprocal and Pythagore identities and then simplify 9 sec x tan x 9 sin x 9 sin x cos x 9 sin x

3x 6 For the function f x x 5 X 5 that is one to one a write an equation for the inverse function in the form y f x b graph f and on the same axes and c give the domain and the range of f and r If the function is not one to one say so a Write an equation for the inverse function in the form y f x Select the correct choice below and if necessary fill in the answer boxes to complete your choice OA x x B The function is not one to one

Determine whether the given function is one to one If it is 656 16 810 1 2 5 5 3 3 1 6 5 is the function f 2 5 5 3 3 1 6 5 one to one Yes No

y r x b graph f and on the same axes and c give the domain and the range of f and if the function is not one to one say so 1 x x 5 a Write an equation for the inverse function in the form y ro Select the correct choice below and if necessary fill in any answer boxes to complete your choice A The function f x is one to one and r x Simplify your answer B The function is not one to one

If a function f has an inverse and f 3 6 then 6 If a function t has an inverse and 1 3 6 then f 6

Rewrite the expression as a single logarithm and simplify the result Hint Begin by using the properties of logarithms 7 In cot ti 7 In 1 tan t

Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f Enter your answers as a comma separated list If an answer does not exist enter DNE if 1 x 0 x if 0 x 1 f x 8 9x absolute maximum value absolute minimum value local maximum value s local minimum value s Submit Answer Need Help Read It 3 0 11 Points Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not print DETAILS SCALCET9 4 XP 1 022 JE DUB

Use the trigonometric substitution to write the algebraic expression as a trigonometric function of 0 where 0 0 i 2 16 x x 4 cos 0

b lim tanh x 8118 12 0 17 Points Use the definitions of the hyperbolic functions to find each of the following limits If the limit is infinite enter co or co as appropriate If the limit does not otherwise exist enter DNE a lim tanh x X18 c lim sinh x X18 d lim sinh x X 00 e lim sech x X 00 DETAILS SCALC lim coth x X18 195 1

7 Your favorite store sends out coupons in the mail Coupon 1 is for 5 off your next purchase Coupon 2 is a 20 off coupon applied to your total purchase Let x the total cost of your purchase at the store a Write a function f x to represent the cost of your purchase using Coupon 1 b Write a function g x to represent the cost of yoru purchase using Coupon 2 c Find f g 75 and explain what this means in context d Find g f 75 and explain what this means in context e In which orer would you like the coupons applied for YOUR order Why

Find the critical numbers of the function Enter your answers as a comma separated list If an answer does not exist enter DNE F x x4 5 x 1 X Need Help Read It Watch It

Find the absolute maximum and absolute minimum values of f on the given interva f t 2 cos t sin 2t absolute minimum value absolute maximum value 0 EN

DETAILS 3 0 11 Points Use the graph to state the absolute and local maximum and minimum values of the function Assume each point lies on the gridlines Enter your answers as a comma separated list If an answer does not exist enter DNE y 5 ww y f x 24 1 absolute maximum value absolute minimum value local maximum value s local minimum value s SCALCET9 4 1 005 2 3 4 5 6 X

J 1 Find the following using the table below X 1 2 3 4 f x 2 3 4 1 f x 1 4 2 3 g x 1 2 4 3 g x 3 4 1 2 h 1 if h x h 1 if h x f x g x f x g x h 1 if h x f g x Question Hel 6 question

Question 18 4 3 2 middle 2 highest 2 7 1 3 v 18x For the above rational function f x 4x 2 5 identify its three inflection points algebrically using its derivatives Leave answers in 4 decimal places when appropriate lowest

Find the absolute maximum and absolute minimum values of f on the given interval f x 6x 18x 54x 5 2 4 absolute minimum value absolute maximum value

e the identity tanh x tanh x 1 tanh x e2x 1 tanh x 1 11 11 cosh x cosh x 2x cosh x e x cosh x 1 ex x ex e x 1 ex e x

Find the numerical value of each expression Round your answers to five decimal places a sinh 2 b sinh In 2

Find the derivative y x y ecosh 8x

For each of the numbers a b c d r and s state whether the function whose graph is shown has an absolute maximum or minimum a local maximum or minimum or neither a maximum nor a minimum Enter your answers as a comind ab cdr IMM E absolute maximum absolute minimum local maximum local minimum neither a maximum nor a minimum

If cosh x sinh x tanh x coth x sech x csch x and x 0 find the values of the other hyperbolic functions at

Prove the identity cosh x sinh x e First use the definitions of the hyperbolic functions and then simplify by combining the exponential terr e 1 cosh x sinh x ex e x 12 1 et

Find the derivative g x g x sinh2 x