Calculus Questions

In the triangle below x 8 Use the Law of Cosines to solve the triangle Round your answers to two decimal places A 8 C 12 cm B 18 cm x cm C

sin 0 2 25 csc Type an integer or a fraction

Click here to watch the video Sketch an angle 8 in standard position such that 0 has the least possible positive measure and the point 0 5 is on the terminal side of 0 Then find the values of the six trigonometric functions for the ang Rationalize denominators if applicable Do not use a calculator Choose the correct graph below A Ay Q Q OB F SUTHY Q 5 O C OU

3 For f x 2x 16x 5 find the following A f x B The slope of the graph of f at x 2 C The equation of the tangent line at x 2 D The value s of x where the tangent line is horizontal PODER PUPAS A f x B At x 2 the slope of the graph of f is C At x 2 the equation of the tangent line is y D The tangent line is horizontal at x Use a comma to separate answers as needed somligar www

Use the Law of Cosines to solve the triangle Round your answers to two decimal places C 106 a 10 b 7 A B

Graph the function over a one period interval y tan O A Which graph below shows one period of the function 1 I X 7 14 video 14 Q Q G OB Q ISA G C O C Q 76 17x 12 3 1 OD

Find the limits in a through c below for the function f x OA lim f x Simplify your answer X 6 A lim f x Simplify your answer X 6 OB The limit does not exist and is neither b Select the correct choice below and fill in any answer boxes in your choice A lim f x x 3x 18 X 6 Simplify your answer o nor o Use co and co when appropriate OB The limit does not exist and is neither co nor o c Select the correct choice below and fill in any answer boxes in your choice

Rewrite the function using the power reducing formulas f x 4 sin x f x X Use a graphing utility to graph the function y 1 5 1 0 0 5 1 5 1 00 5 2 2 2 2 0 5 1 0 0 5 1 5 1 0 1 5 1 5 1 0 0 5 1 5 1 0 0 5 4 y 2 2 y 2 2 0 5 1 0 0 5 1 0

The total sales of a company in millions of dollars t months from now are given by S t 0 031 0 5t 4t 2 A Find S t B Find S 6 and S 6 to two decimal places C Interpret S 10 122 00 and S 10 23 00 A S t B S 6 S 6 C Choose the correct interpretation of S 10 122 00 www OA In approximately 122 months the sales will be 10 million dollars OB The total sales 10 months from now will be 122 00 million dollars OC In 10 months the sales will be increasing at a rate of 122 00 million per month In approximately 122 months the sales will be increasing by 10 million per month

SHORT ANSWER Show all work for full credit 23 Find the total distance traveled by a particle on the x axis with velocity given by v x 3sin 2x for the interval 0 2 5 23

The total cost in dollars of producing x food processors is C x 2100 40x 0 2x A Find the exact cost of producing the 41st food processor B Use the marginal cost to approximate the cost of producing the 41st food processor A The exact cost of producing the 41st food processor is B Using the marginal cost the approximate cost of producing the 41st food processor is

1 y cscx CSC 1 a The period of y cscx is 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression 1 b The phase shift of y csc x is 0 Type an exact answer using as needed Use integers or fractions for any numbers in the expression 1 c The range of y CSC X IS 2 Type your answer in interval notation Use integers or fractions for any numbers in the expression

Use the half angle formulas to determine the exact values of the sine cosine and tangent expressions of the following angle 165 5 sin 165 7 cos 165 5 tan 165 X X Xx

Write an equation of the slant or nonlinear asymptote 20x 19x 23x 4 4x 7x 1 p x The Choose one asymptote is y 010

y 6 csc zx www a The period of y 6 6 csc x is csc Type an exact answer using as needed Use integers or fractions for any numbers in the expression

Use the figure and trigonometric identities to find the exact value of the trigonometric function below in two ways B4 4 cos x sin 3 4 cos x sin 3 12 4 cos x sin 3 4 cot 7 2 x sin 7 2 B

y cscx B phase shift if any and c range of the following function 1 a The period of y CSC X is 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression

Click here to watch the video Find the reference angle for the angle 223 The reference angle is Type an exact answer

Click here to watch the video Write tan 0 in terms of sec 0 if 0 is acute tan 0 expression

The total sales of a company in millions of dollars t months from now are given by the following formu S t 7 t 1 A Use the four step process to find S t B Find S 15 and S 15 C Use the results in part B to estimate the total sales after 16 months and 17 months A S t B S 15 Type an integer or a decimal S 15 Type an integer or a decimal C S 16 Type an integer or a decimal S 17 Type an integer or a decimal

Find d dx 2 d 2x dx 3 2x 3 5 2 7x 5 2 7x 7

Use the figure to find the exact value of each trigonometric function a sin b cos 7 sec 1 csc 2 X X X x x 9 2 sin cos x 24 0 7

Use the graph of the function f shown to estimate the indicated limits and the function value Complete parts A through D OA f 4 Type an integer 4 B The function is not defined at x 4 Af x 4 2 D Find the function value f 4 Select the correct choice below and if necessary fill in the answer box to complete your choice G

Refer to the graph of y f x to the right to describe the behavior of lim f x Use co and co where appropriate x 1 Select the correct choice below and fill in any answer boxes in your choice OA lim f x x 1 OB The limit does not exist and is neither co nor co 10 8 6 Ay 10 10

Find the indicated derivative P d du 9u04 6u 4 te balone Marilia Hant

Use the graph of the function f shown to the right to estimate the indicated function values and limits Complete parts A through E lim f x M A Find the value of lim f x Select the correct choice below and if necessary fill in the answer box to complete x 3 your choice OA x 3 Z OB The limit does not exist B Find the value of lim f x Select the correct choice below and if necessary fill in the answer box to complete

Use the four step process to find f x and then find f 1 f 2 and f 3 f x 2x x 1 f x f 1 f 2 f 3 Type an integer or a simplified fraction Type an integer or a simplified fraction Type an integer or a simplified fraction

To get a flat uniform cylindrical satellite spinning at the correct rate engineers fire four tangential rockets as shown in the figure Figure 1 Suppose that the satellite has a mass of 1200 kg and a radius of 3 0 m and that the rockets each add a mass of 250 kg Figure R 1 of 1 End view of cylindrical satellite Part A What is the steady force required of each rocket if the satellite is to reach 3 rpm in 4 5 min starting from rest Express your answer to two significant figures and include the appropriate units F A Value Submit Request Answer Provide Feedback Units Nex

Use the graph of the function f shown to the right to estimate the indicated function values and limits Complete parts A through E E Is f continuous at x 3 Explain OA The function is continuous OB The function is discontinuous at x 3 since lim f x f 3 X 3 OC The function is discontinuous at x 3 since f 3 does not exist OD The function is discontinuous at x 3 since lim f x does not exist k Q Q G

Find the critical number of the function f x 3x 7x X

The sum of the squares of two negative numbers is 117 and the difference of the squares of the numbers is 45 Find the umbers If there is more than one pair use the or button The pair s of numbers and 0 010 S

Perform the elementary row operation 3R R R on the given matrix Write numbers as integers or simplified fractions 3 1 4 14 2 1 2 3 Resulting matrix

Consider the function f x 4 2 8 on the interval 2 7 A Find the average or mean slope of the function on this interval Average Slope B By the Mean Value Theorem we know there exists at least one c in the open interval 2 7 such that f c is equal to this mean slope Find all values of that work and list them separated by commas in the box below List of values

Refer to functions m and n Find the function m intervals as an integer or a simplified fraction m x x 8 n x x 7 Part 0 2 Part 1 of 2 n x and write the domain in interval notation Write any numb

The floor of a rectangular bedroom requires 210 ft of carpeting Molding is placed around the base of the floor except at two 3 ft doorways If 52 ft of molding is required around the base of the floor determine the dimensions of the floor 3 ft 3 ft

21 Given the velocity and initial position of a body moving along a coordinate line at time t find the position of the body as a function of time 8 V TO 4t sin 41 S 7 2 T A S 2 cos 4t 8 C s 2 cos 4 3 T B s 2 cos 41 4 TU 4t D s 2 cos 4 T 21

Refer to the functions f and g and evaluate the function for the given value of x Select Undefined if applicable f 6 5 5 8 6 3 2 2 4 6 and g 3 4 4 7 0 2 2 5 8 1 6 is f Undefined

the problem 20 Given the acceleration initial velocity and initial position of a body moving along a coordinate line at time t find the body s position at time t a 12 v 0 2 s 0 6 A s 61 2t 6 B s 12t 2t 6 C s 6t 2t 6 D S 6t 2t 20

ex dx 1 e2x A sin 1 ex C C 2 1 e2x C B sec 1 ex D ex sin 1 ex

Does there exist a continuous function f x such that f 0 6 f 2 10 and f x 7 for all a in 0 2

Find all critical numbers for the function and then list them separated by commas in the box below List of critical numbers Hint There are three critical numbers f x x 13 x 1

Find the absolute maximum and absolute minimum values of the function on the interval 2 5 4 Enter 1000 for any absolute extrema that does not exist Absolute maximum Absolute minimum 6 f x 26 X

Consider the function f x on the interval 3 6 A Find the average or mean slope of the function on this interval Average Slope B By the Mean Value Theorem we know there exists a c in the open interval 3 6 such that f c is equal to this mean slope Find all values of c that w and list them separated by commas in the box below List of values

Consider the function f x 5x 4x on the interval 5 5 A Find the average or mean slope of the function on this interval Average Slope B By the Mean Value Theorem we know there exists at least one c in the open interval 5 5 such that f c is equal to this mean slope Find all values c that work and list them separated by commas in the box below List of values

Consider the function f x 2 8x on the interval 2 8 A Find the average or mean slope of the function on this interval i e 8 f 2 8 2 B By the Mean Value Theorem we know there exists a c in the open interval 2 8 such that f c is equal to this mean slope For this problem there one c that works Find it C

By applying Rolle s theorem check whether it is possible that the function f x x x 12 has two real roots Final answer input possible or impossible Answer this part last after you have throught through the reasons below Your reason is that if f x has two real roots then by Rolle s theorem f x must be input a number here at a certain value of x between these two roots but f x is always input negative positive or zero

Consider the function f 2 x 42 9 on the interval 0 4 Verify that this function satisfies the three hypotheses of Rolle s Theorem on the inverval f x is on 0 4 answer is a word f x is on 0 4 answer is a word and f 0 f 4 answer is a number Then by Rolle s theorem there exists a e such that f c 0 Find the value c C

roblem 2 Find an expression for the area under the graph of f x 112 6 on the interval 5 10 D lim 81x A lim 72 00 G lim n 5i n 11 5 1 6 5 5 i 1 11 5 SWI SWI WI Problem 2 Colect i 1 i 1 10 n 5 10i n 11 5 0 6 5 n 5 10i 5 n n 11 5 0i 6 n B lim n x 10i H lim n n E lim n n n 5i 5 n 11 5 5 6 n 5 5i n 5i n 11 i 6 n n C lim n co 11 5 6 n 10 n 10i n 11 5 0i 6 n 5 n F lim t 10 11 10 6 i 1 10i n

Problem 5 The graph off is given to the right Let g x f 1 di 3 a Find g 1 b Find g 2 c Find gr 1 d On what interval is g increasing 3 X f x 2 3 2 1 1 0 1 2 3 1 2 3

Problem 4 Evaluate the following integrals by interpreting them in terms of areas a 5 1x 51 dx 7 49 x dx