Calculus Questions

Problem 5 Find an integral which represents the volume of the solid obtained by rotating the region enclosed by the curves y x 2 and y 2x 8 about the x axis A E 7 x H x 2x 8 dx B 7 2x 8 x2 2 dx C Problem 5 Select 2x 8 dx F 2x 8 dx F x 2x x4 2x 8 dix 4 2 2 2x 8 x D 10 S x 2x 8 x G 2x 8 x dx 2x 8 x dx

Problem 3 Which of the following represents the area of the region enclosed by the curves y x and y 2x 8 for 3 x 4 A 3 x 2x 8 dx C 2 3 x2 2x 8 dx H F x 2x 8 dx E x2 2x 8 dx x 2x x 2x 8 dx dx 2 x 2x 8 B x 2x 8 2 2 2 1 x 2x 8 dx D 2 x 2x 8 dx 3 x 2x 8 dx x 2x 8 dx G G x 2x 8 dx 3 x x 2x 8 dx 2 2x 8 dx x 2x 8 dx

Problem 2 Evaluate the following integrals Jos a 3 c b 2 0 In x 2 X TU 3 0 dx cos x V1 6 sin x dx sin 8 sec e de cos 8

Problem 8 Suppose that the temperature of a cup of coffee t minutes after it is poured is given by T t 24 77e kt where k 4 Find the average temperature of the coffee during the first 37 minutes after it is poured Enter YOUT

Problem 1 Evaluate the following integrals 1 S 5x 177 2 dbx a b je Sesved 4

1 Define f x 2 for x in 0 1 5 f x 0 for x outside of 0 1 5 Find the area between f x and the x axis over the entire real line Answer

Write an equation for the function graphed here 5 4 3 2 f x 3 2 1 2 3 3

The top and bottom margins of a poster are 2 cm and the side margins are each 4 cm If the area of printed material on the poster is fixed at 390 square centimeters find the dimensions of the poster with the smallest area Width Height

COS COS COS 3 4x COS 3 Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression

cos arcsin u CHE cos arcsin u Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationa all denominators

sin sin 1 sin sin 1 Type an exact answer using radicals as needed Rationalize all denominators

tan arccos 5 an arccos Type an integer or a simplified fraction

y sec 2 HECH y Type an exact answer using as needed Use integers or fractions for any numbers in the expression

watch the video that describes finding inverse sine values Click here to watch the video Find the exact value of the expression sin 9 sin 12 0 Type an exact answer using x as m

xact value of the expression sin 2 sin 2 Type an exact answer using as needed

expression cos m2 2 Type an exact answer using x as

9x 49 441 0 a Find the standard form of the equation of the ellipse b Find the center vertices foci and eccentricity of the ellipse Order your answers from smallest to largest x then from smallest to largest y If the ellipse is degenerate find its center then enter NONE in each center vertices foci eccentricity x y x y c Select the correct graph of the ellipse Use a graphing utility to verify your answer y 10 10 10 10 10 10 10 O

If a function f has an inverse and f x 1 then f 1 If a function f has an inverse and f x 1 then f 1

Complete the statement y cos 1 x means that x y cos x means that x for 0 y t for 0 syst

Watch the video that describes finding inverse function values Click here to watch the video Find the exact value in radians of the expression cot 1 3 3 cot 1 Type an exact answer using as n

K Watch the video that describes finding inverse cosine values Click here to watch the video Find the exact value of the expression arccos arccos Type an exact answer using a

Find the center vertices foci and eccentricity of the ellipse Order your answers from smallest to largest x then from smallest to large y 5 x 5 1 1 4 Center Vertices Foci Eccentricity Select the correct graph of the ellipse Use a graphing utility to verify your answer 10 4 10 6 4 fo

Find the standard form of the equation of the ellipse with the given characteristics y 1 3 3 5 2 5 4 7 3

A boat sails directly toward a 150 m skyscraper that stands on the edge of a harbor The angular size of the building is the angle formed by lines from the top and bottom of the building to the observer see figure Complete parts a and b below Round to five decimal places as needed de b Graph as a function of x and determine the point at which the angular size changes most rapidly Choose the correct graph below dx OA Q OB 0 1000 by 0 0 008 REISSE 0 1000 by 0 0 008 For what value of x is the angular size changing most rapidly x Round to the nearest integer as needed M 0 1000 by 0 008 01 OD 150 m S 0 1000 by 0 008 01

Find two numbers A and B with AB whose difference is 44 and whose product is minimizec A B

Find an equation of the ellipse with the given characteristics Vertices 0 18 eccentricity

Find the eccentricity of the ellipse 2 1 x 25 36

Match the equation with its graph x 16 1 15 10 5 15 10 5 y 15 10 5 10 15 10 10 5 5 10 15 10 15 X 15 10 15 10 5 5 15 10 0 5 10 15 y y 15 10 5 10 15 5 10 15 5 10 15 X

wy oc cos 0 Yo Find the derivative of the inverse cosine using the theorem of the derivative of the inverse function The theorem states let f be differentiable and have an inverse on an interval 1 If x a point of I at which f x 0 then f isdifferentiable at yo Rx and Y x sin xo 1 sin xo Part 2 of 6 R 00 cos 0 How can the expression on the right side be rewritten in terms of f x OA Substitute using xocos Yo OB Substitute using Yo cos xo OC Rewrite the expression using cac Xosin xo OD Substitute using the identity sinx cos 1 sin xo HW Score 60 58 13 93 of 23 points O Points 0 of 1 CITES Save

A parcel delivery service will deliver a package only if the length plus the girth distance around does not exceed 120 inches Find the maximum volume of a rectangular box with square ends that satisfies the delivery company s requirements Maximum Volume

Find the vertex focus and directrix of the parabola and sketch its graph Use a graphing utility to verify your graph x 20 y 5 vertex focus directrix No Solution x y 10 323 40 la 4 7 9 10 Fill Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties

A boat is towed toward a dock by a cable attached to a winch that stands 10 ft above the water level see figure Let 0 be the angle of elevation of the winch and let L be the length of the cable as the boat is towed toward the dock Complete parts a to c below When L 50 ft When L 20 ft 37 When lim de dL de dl de nL 11 ft 0 1984 Round to four decimal places as needed dL 0 0041 Round to four decimal places as needed de 0 0289 Round to four decimal places as needed dL de c Find lim and explain what is happening as the last foot of cable is reeled in note that the boat is at the dock when L 10 What is the value of the limit dl L 10 10 ft Simplify your answer

Find the x and y intercepts of the graph of the circle If an answer does not exist enter DNE x 10x y 2y 19 0 STEP 1 Consider the equation for the circle x2 10x y2 2y 19 0 Let y 0 Give the resulting equation below STEP 2 Solve your equation from Step 1 for x If one or more solutions exist these values are the x coordinates of the x intercepts of the graph of the circle Enter your answers as a comma separated list X STEP 3 Consider once again the equation for the circle x2 10x y2 2y 190 Now let x 0 Give the resulting equation below STEP 4 Solve your equation from Step 3 for y If one or more solutions exist these values are the y coordinates of the y intercepts of the graph of the circle Enter your answers as a comma separated list y STEP 5 Complete the problem by listing the x and y intercepts x y x intercepts y intercept x y x y smaller x value larger x value

K Prove the following identity and give the values of x for which it is true COS os sinx 2 1 08 2 c 2x Simplity sin sin x s n nh n sin de TR

Given the following information evaluate the other five functions RECU and 0 so cos sin 0 35 tan 8 45 4 3 csc 8

Find the standard form of the equation of the parabola with the given graph 6 5 4 2 6 3 2 1 T y 11 9 7 5 3 1 3 5 7 9 11 0 0 1 2

Match each equation with its graph 5 A A 7 N 2 y Yx 2 B 2 y 7 ay

A woman pulls a sled which together with its load has a mass of m kg If her arm makes an angle of with her body assumed vertical and the coefficient of friction a positive constant is u the least force F she must exert to move the sled is given by mgu sin cos 0 If 0 15 find the maximum and minimum values of F for 0 0 T 2 Your answers will involve the unspecified constants m and 9 maximum force minimum force Newtons Newtons F

A rectangular storage container with an open top is to have a volume of 60 cubic meters The length of its base is twice the width Material for the base costs 60 dollars per square meter Material for the sides costs 6 dollars per square meter Find the cost of materials for the cheapest such container Minimum cost

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle What is the area of the largest possibe Norman window with a perimeter of 44 feet

2200cm of material is available to make a box with a square base and an open top find the largest possible volume of the box Volume cm

Find the length L and width W with W L of the rectangle with perimeter 44 that has maximum area and then find the maximum area L W Maximum area

How would you divide a 16 inch line into two parts of length A and B so that A B 16 and the product AB is maximized Assume that A B A B

se the graph of f x to discuss the graph of y f x Organize your conclusions in a table and sketch a possible graph of y f x Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f has inflection points at x Use a comma to separate answers as needed OB The function f has no inflection points Choose the correct graph of y f x below OA M OB 1 GEXER G OC A Q OD MD

Antua 9 h D Identify intervals on which f x 0 Choose the correct answer below OA a c c e g h OC d e g h OE b c c e g h OG a b d e g h E Identify intervals on which f x is increasing Choose the correct answer below OA d e g h OC a b e g OE e g O B a b e g OD e g OF a c c d e g OH f x 0 over a h OB a c c e g h OD b c c e g h OF a b d e g h

Use the graph of y f x assuming f x 0 if x b ord and f x 0 if x 1 to answer parts A through F ANTA E Identify intervals on which f x is increasing Choose the correct answer below OA d e g h C a b e g CHOKES OE e g OG a c c d e g F Identify intervals on which f x is decreasing Choose the correct answer below OA d e g h OC b c c d e g OE a c c d e g OG b c c e g h OB a c c e g h OD b c c e g h OF a b d e g h OH f x is never increasing on a h OB a b e g OD a c c e g h OF e g OH f x is never decreasing on a h

Use the graph of y f x assuming f x 0 if x b ord and f x 0 if x f to answer parts A through F ANTA AM a E Identify intervals on which f x is increasing Choose the correct answer below OA d e g h OC a b e g OE e g OG a c c d e g F Identify intervals on which f x is decreasing Choose the correct answer below OA d e g h OC b c c d e g OE a c c d e g OB a c c e g h OD b c c e g h OF a b d e g h OH f x is never increasing on a h OB a b e g OD a c c e g h OF e g

Use the graph of y f x assuming f x 0 if x b or d and f x 0 if x f to answer parts A through F AVINA GULB D Identify intervals on which f x 0 Choose the correct answer below OA a c c e g h OC d e g h OE b c c e g h OG a b d e g h E Identify intervals sol which f x is increasing Choose the correct answer below OA d e g h OC a b e g OE e g OG a c c d e g OB a b e g OD e g OF a c c d e g OH f x 0 over a h OB a c c e g h OD b c c e g h OF a b d e g h OH f x is never increasing on a h

In Silicon Valley a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup o the underground contamination Suppose that the required monetary pool in millions of dollars is given by the following function where x is the percentage expressed as a decimal fraction of the total contaminant removed Complete parts A through E 3x P X 1 X 0 x 1 w C Find any horizontal and vertical asymptote Find the vertical asymptote s if any Select the correct choice below and if necessary fill in the answer box to complete your choice CEILE A The vertical asymptote s is are x Simplify your answer Use a comma to separate answers as needed OB There are no vertical asymptotes Find the horizontal asymptote s if any Select the correct choice below and if necessary fill in the answer box to complete your choice OA The horizontal asymptote s is are y Simplify your answer Use a comma to separate answers as needed OB There are no horizontal asymptotes D Find the x and y intercepts Find the x intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice A The x intercept s is are x Simplify your answer Use a comma to separate answers as needed B There are no x intercepts

Use the graph of y f x assuming f x 0 if x b ord and f x 0 if x f to answer parts A through F AVD A D Identify intervals on which f x 0 Choose the correct answer below OA a c c e g h OC d e g h OE b c c e g h OG a b d e g h E Identify intervals on which f x is increasing Choose the correct answer below OA d e g h OC a b e g OE e g OG a c c d e g SLILA food in de Lalain OB a b e g OD e g OF a c c d e g OH f x 0 over a h OB a c c e g h OD b c c e g h OF a b d e g h OH f x is never increasing on a h