Calculus Questions

6 1 X f x f x 2 3 2 a f 4 b f 1 c f 3 d f 3 3 4 13 05 3 7 3 lo 6 8 OA 4 Type an integer or a fraction OB 4 cannot be determined or state that the derivative cannot be determined 2 MA a Choose the correct answer below and if necessary fill in the answer box within your choice

Find all the inverses associated with the following function and state their domains 22x x 22 f x TWEE The inverse s is are f x Type an exact answer using radicals as needed Use a comma to separate answers as needed

nsider the following function Find the inverse function express it as a function of x and find the derivative of the inverse function X x 6 f x 6x9

Find the inverse of the following function and write it in the form f x 3 f x 2 Xx 1 for x 20 The inverse function is f x for 0 x 3

K Find four intervals on which f is one to one making each interval as large as possible Four intervals on which f is one to one are Type your answer in interval notation Use a comma to separate answers as needed

Find the inverse function and graph both f x and f x on the same set of axes Check your work by looking for the required symmetry in the graphs f x 9 8x The inverse function is f x SIER

Find the inverse function on the given interval if specified and graph both f and f on the same set of axes Check by looking for the required symmetry in the graphs f x x 8 for x 8 Find the inverse function f x for x

a Find the inverse of the function below on the given interval and write it in the form y f x b Verify the relationships f f x x and f f x x f x x 6 a f x 0 5 9

K Give an example of a function that is one to one on the entire real number line Choose the correct answer below OA f x sin x 3 OB f x x x 2x O C f x x OD f x 3x 2

3 Refer to the information below A and B are angles in standard position Without using a calculator find the exact value of sin A B sin A 3 5 sin B 12 13 0 A T B 3 2

1 Simplify the expression completely cos sec 3 csc

Let 1 5 and 6 5 0 Compute the dot product 6 b

8x 9x 1 a Find its inverse and check your answer b Find the domain and the range of f and f 1 The function f x is one to one OA The domain is x x Type integers or fractions Use a comma to separate answers as needed B The domain is xx 9 Type integers or fractions Use a comma to separate answers as needed OC The domain is x x Type integers or fractions Use a comma to separate answers as needed OD The domain is the set of all real numbers Find the range of f Select the correct choice below and if necessary fill in the answer box to complete your choice OA The range is yly Type integers or fractions Use a comma to separate answers as needed OB The range is yly Type integers or fractions Use a comma to separate answers as needed OC The range is ylys Type integers or fractions Use a comma to separate answers as needed D The range is the set of all real numbers S

Given p 5 7 and 4 4 find p 4u p 4u

Given p 6 2 and 6 10 5 find p b 7 6

Given 1 8 and 3 1 find b a b g

Given a 22 33 and 6 37 3 find a b a b 3

Perform the vector addition 12 5 7 4

2 Here is a polygon A D B C a Draw the dilation of ABCD using center A and scale factor Label the dilation EFGH b Draw the dilation of ABCD with center D and scale factor Label the dilation IJKL

4 List the intervals for each section of the function and state whether it is increasing decreasing or constant Label them A E starting from left to right on the graph A B C D E Distance km 70 60 50 40 30 20 10 10 00 11 00 2 00 13 00 The Which interval has the fastest speed What is the speed on this interval 14 00 In a couple sentences write a story describing what this graph could represent Include a description for each interval

A water tank shown to the right is shaped like an inverted cone with height 4 m and base radius 1 m a If the tank is full how much work is required to pump the water to the level of the top of the tank and out of the tank Use 1000 kg m for the density of 2 water and 9 8 m s for the acceleration due to gravity b Is it true that it takes half as much work to pump all the water out of the tank when it is filled to half its depth as when it is full Explain a Draw a y axis in the vertical direction parallel to gravity and choose the bottom of the tank as the origin For 0 y 4 find the cross sectional area A y in terms of y 16 2 A y 1000x h 20 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 4 m

3 The function f x x 3 is one to one a Find the inverse of f and check the answer b Find the domain and the range of f and f c Graph f f1 and y x on the same coordinate axes and if necessary fill in the answer box to complete your choice A The domain is x x B The domain is x x C The domain is x x D The domain is the set of all real numbers Find the range of f if necessary fill in the Select the correct choice below and answer box to complete your choice 1 c Graph f f and y x on the same coordinate axes The graph of y x is shown using dashed line Choose the correct graph below OA O C B D E

6 The function f x is one to one 5 X a Find its inverse and check your answer b Find the domain and the range of f and f a f x 5 Simplify your answer 6 X b Find the domain of f Select the correct choice below and if necessary fill in the answer box to complete yo choice O A The domain is x x Type integers or fractions Use a comma to separate answers as needed OB The domain is x x Type integers or fractions Use a comma to separate answers as needed OC The domain is x x Type integers or fractions Use a comma to separate answers as needed D The domain is the set of all real numbers

The graph of a one to one function is shown to the right Draw the graph of the inverse function f 1 Choose the correct graph of the inverse function f OA OB below 5 O D E C

1 Consider the functions f x 5x 5 and g x x 5 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other Use a comma to separate answers as needed B No values should be excluded from the domain OA x b What is g f x g f x X Simplify your answer Give any values of x that need to be excluded from g f x Select the correct choice below and fill in any answer boxes within your choice Use a comma to separate answers as needed B No values should be excluded from the domain 1 2 of 3 c Are the functions f and g inverses of each other Choose the correct answer below Yes No Save for the centra Previous

1 Consider the functions f x 5x 5 and g x 5 x 5 a Find f g x b Find g f x c Determine whether the functions f and g are inverses of each other a What is f g x f g x X Simplify your answer Give any values of x that need to be excluded from f g x Select the correct choice below and fill in any answer boxes within your choice A x Use a comma to separate answers as needed B No values should be excluded from the domain b What is g f x

Find the inverse of the one to one function State the domain and the range of the inverse function 10 15 9 11 8 14 7 13 6 15 The inverse function is Type an ordered pair Use a comma to separate answers as needed

sentence below If the domain of a one to one function f is 1 00 the range of its inverse f is 1 If the domain of a one to one function f is 1 00 the range of its inverse f is 1 0 00 m 11

For f x a fog 2 X 9 a fog x A and g x b gof 2X 5 9X X find the following composite functions and state the domain of each c fof d gog Simplify your answer Select the correct choice below and fill in any answer boxes within your choice The domain of fogis x x 0 x s x ww 5 1 Type an inequality Use integers or fractions for any numbers in the expression Use a comma to separate answers as needed B The domain off og is all real numbers 4 2 x 9 b gof x 2 9x 81 Simplify your answer Use integers or fractions for any numbers in the expression

Use Newton s method to find all roots of the equation correct to eight decimal places Start by drawing a graph to find initial approximations Enter your answers as a comma separated list earctan 3x 27x 1 X

A graphing calculator is recommended A company generates a continuous stream of income of 22t million dollars per year where t is the number of years that the company has been in operation a Find the integral for the present value of this stream for the first 6 years at 6 interest compounded continuously Do not use a graphing calculator 6 S PV t dt b Evaluate your answer to part a using FnInt on a graphing calculator Enter your answer in millions of dollars Round your answer to the nearest whole number million

Find the degree measure of each angle without using a calculator Check your answers using a graphing calculator a 11 3 660 b 4 720 c 2 1 14159 X

If the shortest side of a 30 60 90 triangle has length 500 kilometers then what is the length of the longest side km

Find the distance along the surface of the earth between City A and City B if the two cities determine a central angle of 0 88 radian Assume that the earth is a sphere of radius 4000 miles mi

3 3 12 6 12 3 f x g x y g x 3 X 1 3 3 12 y f x

A graphing calculator is recommended Radioactive waste is leaking out of cement storage vessels at the rate of te0 19t hundred gallons per month where it is the number of months since the leak began Find the total leakage in gallons during the first 2 months Verify your answer using FnInt on a graphing calculator Round your answer to the nearest whole number gallons

Find the size of the permanent endowment in dollars needed to generate an annual 8 000 forever at an interest rate of 4 compounded continuously Round your answer to the nearest whole number

Use the following functions f x x 4 and g x x 2 to solve each of the following 5 f x 0 7 f x g x x 4 x 2 x 4 0 4 4 x 6 g x 0 X 2 0 2 a X 2

2 11 x 3x 10 0

Use the figure to solve each inequality yo 5 1 0 4 2 1 g x 0 1 4 00 2 g x 0 1 5 5 4 0 2 X y g x

12 x 7x 12

Use the following functions f x x 4 and g x x 2 to solve cach of the following 10 f x g x 8 f x 0 9 g x 0

2 Use the following functions f x x 4 and g x x 2 to solve each of the following 5 f x 0 6 g x 0 7 f x g x

Fuerza El ctrica 2 Determine la fuerza el ctrica experimentada por la carga q 1 00 C en el arreglo que se muestra en la figura si Q 2 00 C y a 0 250m Q a a a Q

2 Here is triangle ABC Triangle XYZ is similar to ABC with scale factor 7 A 5 C B 4 a Draw what triangle XYZ might look like b How do the angle measures of triangle XYZ compare to triangle ABC Explain

A C E 1 y x 2 2 9x 4y z 1 B D F

Given that cos 0 and sin 0 0 determine the values of the sine and cosine functions for 20 41 sin 20 Type a simplified fraction

Match the surfaces with the appropriate description horizontal plane non horizo paraboloid hyperbolic paraboloid cone hyperboloid of one sheet or hyperbolon Note Make sure that you can sketch each of these surfaces paying special attent 1 x 2y 3z VENERE hyperbolic paraboloid horizontal plane non horizontal plane circular cylinder parabolic cylinder ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid one sheet hyperboloid two sheets V V 2 z6x 2y 3 z y 3x V 4 z 3 5 3x 6y2 22z 4 6 6y z 4 7 z 6x 2y 8 y 62 9 y x 2

the appropriate description horizonta paraboloid hyperbolic paraboloid cone hyperboloid of one sh Note Make sure that you can sketch each of these surfaces pa 1 x 2y 3z Che horizontal plane non horizontal plane circular cylinder parabolic cylinder ellipsoid elliptic paraboloid hyperbolic paraboloid cone hyperboloid one sheet v 2 z 6x 2y 3 z y 3x 4 z 3 5 3x 6y 2z 4 6 2 6y 2 4 7 z 6x 2y

K expres 2 sin 55 cos 99 2 sin 55 cos 99 Do not include the degree symbol in your answer