# Calculus Questions

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Calculus
Limits & Continuity
Suppose that f x ln 5x 4 Find f x and use interval notation to give the domain of f Note When entering interval notation in WeBWork use I for o I for co and U for the union symbol If the set is empty enter without the quotation ma Domain
Calculus
Definite Integrals
Evaluate the definite integral
Calculus
Application of derivatives
Let Use logarithmic differentiation to determine the derivative f x f x x5 x 4 x 9
Calculus
Application of derivatives
Evaluate the definite integral 522 5 4 S 8 TERMEN dx
Calculus
Definite Integrals
Use the washer method to find the volume of a shifted solid of revolution Question Find the volume of a solid of revolution formed by revolving the region bounded above by the graph of f x 3x 1 an below by the x axis over the interval 5 6 about the line y 4 Enter an exact value in terms of Provide your answer below
Calculus
Differentiation
If f x 4 cos 2 ln x find f x
Calculus
Application of derivatives
Sketch an angle 0 in standard position such that has the least possible positive measure and the point 1 0 is on the terminal side of 0 Then find the values of the six trigonometric functions for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below O A Q O B 2 O C
Calculus
Application of derivatives
Sketch an angle 0 in standard position such that has the least possible positive measure and the point 0 2 is on the terminal side of 0 Then find the values of the six trigonometric functions for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below O A N 4 OB 6 Ay O C 6 O
Calculus
Application of derivatives
Sketch an angle 0 in standard position such that has the least possible positive measure and the point 12 35 is on the terminal side of 0 Then find the values of the six trigonometric functions for the angle Rationalize denominators when applicable Do not use a calculator Choose the correct graph below O A 25 Q O B Ay 40 oo O C Ay Q
Calculus
Application of derivatives
Sketch an angle 0 in standard position such that has the least possible positive measure and the point 5 12 is on the terminal side of 0 Then find the values of t trigonometric functions for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below A 18 OB 117 Ay 1 OC 18 Q
Calculus
Definite Integrals
Evaluate the definite integral 11 12 x 3 da
Calculus
Indefinite Integration
Evaluate the indefinite integral S 11
Calculus
Indefinite Integration
Evaluate the indefinite integral
Calculus
Application of derivatives
The value of e that satisty the conclusion of the mean value theorem for f x 1 3 Select one On 2 Ob 2 0 OC Od 3 Oe 3 NONE
Calculus
Differentiation
f x f e f x
Calculus
Differentiation
Find f x if x 4 f x In
Calculus
Definite Integrals
Y TO 8 10 12 14 16 Years after 1980 G ue curve shows national health expenditures in billions of dollars The red curve shows its derivative Next question National health expenditures in billions of dollars from 1980 to 1994 are given by the function f t in the graph to the left a How much money was being spent at the beginning of 1983 700 billion b Approximately how fast was the rate of spending increasing in 1990 billion per year
Calculus
Differential equations
Let f x be the number in thousands of computers sold when the price is x hundred dollars per computer Interpret the statements f 14 80 and f 14 2 Then estimate the number of computers sold if the price is set at 1425 per computer KIZB What does f 14 80 imply OA When the price per computer is 1400 for every 100 price increase the sales increase by 80 000 computers B 80 000 computers are sold when the price is set at 1400 OC When the price per computer is 8000 for every 100 price increase the sales increase by 14 000 computers D 80 000 computers are sold when the price is set at 140 What does f 14 2 imply OA When the price per computer is 1400 for every 1000 price increase the sales decrease by 2 000 computers c When the price per computer is 1400 for every 100 price increase the sales decrease by 2 000 computers If computers are sold for 1425 per computer 79 5 computers will be sold OB 14 000 computers are sold when the price is reduced by 200 OD 2 000 computers are sold when the price is set at 1400
Calculus
Differentiation
Suppose that f 600 6000 and f 600 10 Estimate each of the following b f 600 5 c f 599 e f 599 75 a f 601 d f 598 a f 601 b f 600 5 6010 Simplify your answer Type an exact answer Simplify your answer Type an exact answer
Calculus
Vector Calculus
Question A solid is formed by rotating the region bounded by the graphs of y x y 24 and x 13 in the first quadrant about the line x 5 Which of the following gives the volume of the solid Select the correct answer below 24 17 2 169 10 J J JU 24 169 10 2 10y 8 169 dy 2 10y 5 64 dy 24 10y 18 169 dy 24 10y 13 64 dy
Calculus
Limits & Continuity
Evaluate the following two limits 1 lim x 2 2 lim x 2 1 x 2 1 x 2
Calculus
Limits & Continuity
2 Use the graph of each translated parent function to write its equation b O PERSEVERE Laura sketches the path of a model rocket that she launches a What type of function does the graph show 3 b In which axis has the parent function been reflected that on has Height m M 2814
Calculus
Application of derivatives
Which description applies to the graph of y3 7 7472 The graph is a translation 7 units right and 7 units up of the graph of y 3 7 The graph has an asymptote at y 7 The domain is all real numbers and the range is y 7 O The graph is a translation 7 units left and 7 units up of the graph of y 3 7 The graph has an asymptote at y 7 The domain is all real numbers and the range is y 7 O The graph is a translation 7 units left and 7 units down of the graph of y 3 7 The graph has an asymptote at y 7 The domain is all real numbers and the range is y 7 The graph is a translation 7 units night and 7 units down of the graph of y 3 7 The graph has an asymptote at y 7 The domain is all real numbers and the range is y 7
Calculus
Definite Integrals
Use a graphing utility to graph the polar equation inner loop of r 8 12 sin 0 Find the area of the given region Round your answer to four decimal places al Enter a number
Calculus
Limits & Continuity
Find the value of c where the table below probability distribution of random variable X X P X X 1 1 6 2 C Malm 4
Calculus
Definite Integrals
a Use the definition of derivative limit process to find f x of the function f x x 2x b Use the result of a to find the equation of the normal line to f at x 1
Calculus
Differentiation
Find the first derivative of each function below x x 1 x a y tan 3x sec 3x b f x c f x xe 1 et 1
Calculus
Differential equations
Show analytically that f is not differentiable at x 0 x 1 f x 2x x 0 x 0
Calculus
Application of derivatives
0 67 1 pt 398 Detai The graph shows the water level in a reservoir as a function of the number of months since the start of the year 100 90 80 70 60 50 40 30 20 10 1 10 1 2 3 4 5 6 7 8 9 10 The highest water level was reached in month reached in month and the lowest water level was
Calculus
Application of derivatives
Question 10 0 1 pt 399 Details The population of a city can be modeled by P t 33e0 05t thousand persons where t is the number of years after 2000 Approximately how rapidly will the city s population be changing in 2023 The population will be changing by thousand persons year Enter your answer rounded to at least three decimal places Question Help Video Written Example Subr
Calculus
Limits & Continuity
Question 7 Suppose f x is continuous everywhere and has the following values 0 30 14 10 10 5 0 1 pt 3299 Details 20 10 I f x Based on this determine what you are willing to guarantee Between 10 and 2 20 you guarai Between 0 and x 10 you guarante Select an answer there is a root nothing Between 2 20 and z 30 you guarantee Select an answer Between z 30 and z 40 you guarantee Select an answer 40 20
Calculus
Limits & Continuity
The graphs of y f x solid and y g x dashed are shown 8 7 6 5 4 3 2 1 Find the following f 3 g 3 f g 3 fg 3 8 1 7 6 5 4 321 1 45 5 6 649 7 8 2 3 4 5 6 7 8
Calculus
Vector Calculus
0 1 pt 399 Details The graph shows the water level in a reservoir as a function of the number of months since the start of the year 100 90 80 70 60 50 40 30 20 10 1 10 1 2 3 4 5 6 7 8 9 10 The highest water level was reached in month the lowest water level was reached in month and
Calculus
Limits & Continuity
Suppose f is defined at x 2 and lim f a exists but lim f x f 2 x 2 x 2 The graph of y f z might look like select all that apply None of these Deta 20
Calculus
Application of derivatives
The following chart shows living wage jobs in a city per 1000 working age adults over a 5 year period Year 1997 1998 1999 2000 2001 635 670 700 720 735 Jobs What is the average rate of change in the number of living wage jobs from 1997 to 1999 Note the units are already included Jobs Year
Calculus
Application of derivatives
Theo and Sasha start at the same place on a straight road riding bikes with the following velocities measured in mi hr Complete parts a through f VT t 5 fort 20 vs t 10t for 0 st 2 and vs t 20 for t 2 Theo Sasha a Graph the velocity functions for both riders Choose the correct graph below OA Av 25 0 0 5 B Av 25 0 OC rides farther Av 25 0 0 b If the riders ride for 2 hr who rides farther Interpret your answer geometrically using the graphs of part a Sasha rides mi and Theo ridesmi Therefore D Av 25 0
Calculus
Limits & Continuity
Suppose f g are continuous functions where f 9 19 and lim 6f x 2g x 122 x 9 Then g 9 Question
Calculus
Limits & Continuity
Consider the graph shown Check all that apply lim f x exists x 2 a f 2 exists None of the above
Calculus
Definite Integrals
The region bounded by the graphs of x 0 x Iny and x 7 6 Iny in the first quadrant is revolved about the y axis What is the volume of the resulting soll The volume is Type an exact answer
Calculus
Limits & Continuity
2x 6 if x 4 Let f x 34 5x if x 4 if x 4 12 eta Determine whether f x is continuous at 4 If f x is not continuous identify why Not continuous f 4 is undefined Not continuous lim f x does not exist x 4 Not continuous lim f x f 4 x 4 The function is continuous at x 4
Calculus
Limits & Continuity
The graph of y f x has the following features lim f x 3 f x 2 f x f x xxx lim TH lim 24 1 lim 1 12 Which of the following might be a graph of y f z 8 78 8543 2 3 2 1 4 3 2 20 Z d a 9 9 4 3 2 3 16 112 84 4 5 6 3 2 8 7 6 4 2 F 2 12 4 4 9 b 8
Calculus
Definite Integrals
Let R be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y O A 1 x 1 B X y 1 revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice dx Type exact answers JOdx dx Type exact answers
Calculus
Application of derivatives
Suppose f x has the following values I 1 9 1 99 1 999 2 1 9 5 99 5 999 C 2 001 2 01 2 1 9 005 9 05 9 5 What value of c would make f x continuous at x 2 Enter a value of c If no value exists enter DNE
Calculus
Limits & Continuity
suppose Iim f x x 2 The graph of y f x might look like select all that apply
Calculus
Application of derivatives
Suppose f x is defined at 1 and lim f x exists but lim 4 1 1 The graph of y f z might look like select all that apply None of these f x f 1
Calculus
Indefinite Integration
Consider the graph shown Check all that apply a f 2 exists lim f x exists 112 None of the above
Calculus
Limits & Continuity
Suppose f x IS The graph of y f x might look like select all that apply Q de x 1 CO
Calculus
Application of derivatives
Let f x 4x 3 if x 1 12 5x if x 1 Determine whether f x is continuous at x 1 If f x is not continuous identify why Not continuous lim x 1 f x f 1 Not continuous f 1 is undefined Not continuous lim f x does not exist x 1 The function is continuous at x 1
Calculus
Application of derivatives
x 1 not exist The graph of y f x might look like select all that apply Q
Calculus
Limits & Continuity
Consider the graph shown Check all that apply f 1 exists lim f x exists x 1 None of the above