Calculus Questions

Find the consumers surplus and the producers surplus at the equilibrium price level for the given price demand and price supply equations Include a graph that identifies the consumers surplus and the producers surplus Round all values to the nearest integer p D x 70 0 04x p S x 20e0 001x What is the consumers surplus CS CS Round to the nearest integer as needed Round all intermediate steps to the nearest integer

Find the value of the summation 3 2k

59 y 3 cos 30 5 3 2 3 60 120 180 240 300 360

Use a graphing calculator to find where the curves intersect and to find the area between the curves y ex y 3x 5x a The left point of intersection is Type integers or decimals rounded to the nearest thousandth as needed Type an ordered pair

Use a graphing calculator to find where the curves intersect and to find the area between the curves y ex y 3x 5x a The left point of intersection is Type integers or decimals rounded to the nearest thousandth as needed Type an ordered pair

Find the period in degrees Then sketch the graph using degrees 54 y tan 0 55 y sin 0 60 120 180 240 300 360 90

For the rectangular coordinates 2 2 2 2 a plot the point and b give two pairs of polar coordinates for the point where 0 0 360 K a Choose the correct plot of 2 2 2 2 below OA Ay B Ay COL O C b Give two pairs of polar coordinates for the point where 0 0 360 Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in degrees Do not include the degree sym Use a comma to separate answers as needed

Use the Fundamental Theorem of Calculus to find the derivative of I 1 f x f x dt 3 1 t5 1 1 x OF

20 points Let C be the curve obtained by going from 0 1 to 1 0 counter clockwise aroun e unit circle Let F x y x y e x y 1 2 e x y 1 2 Compute F F dr

For the point a Choose the graph that represents the point 1 1 37 OA x 2 in polar coordinates a plot the point b give two other pairs of polar coordinates for the point and c give the rectangular coordinates of the point 4 3x 2 Q B x 2 3x 2 0 Q Q OC x 2 3x 2 0 Q b What are the coordinates of the point for which r 0 and 2x 0 4x 11x 4 Type an ordered pair Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression What are the coordinates of the point for which r 0 and 0 0 2x Type an ordered pair Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression OD R 2 3x 2 Q

5 Determine the value of x such that the points A 3 5 B x 7 C 8 10 and D 0 2 form the parallelogram ABCD Hint The order of the letters matters

Watch the video that describes plotting points with polar coordinates Click here to watch the video Plot the point 3 240 Then find the rectangular coordinates of the given point In rectangular coordinates 3 240 is Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Choose the graph OA 180 180 90 270 90 270 0 Q Q OB below 180 180 90 270 90 270 0

An amusement company maintains records for each video game it installs in an arcade Suppose that C t and R t represent the total accumulated costs and revenues in thousands of dollars respectively t years after a particular game has been installed and the derivatives C t and R t are the following functions C t 3 and R t 8 0 3t Find the area between the graphs of C and R over the interval on the t axis from 0 to the useful life of the game and interpret the results What is the useful life of the game t years Round to the nearest tenth as needed

Monthly sales of a particular personal computer are expected to decline at a rate of S t 5te lt computers per month where t is time in months and S t is the number of computers sold each month The company plans to stop manufacturing this computer when monthly sales reach 900 computers If monthly sales now t 0 are 2 000 computers find S t How long to the nearest month will the company continue to manufacture the computer S t

The future value at 7 interest compounded continuously for 5 years of the continuous income stream with rate c 0 02t flow f t 900e is 5 142 Compute the interest earned Type an integer or a decimal ECOD

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line y 2x x 2y about the y axis 107 2 V Sketch the region y 4 3 y f

4 Given u and 7 draw the following vectors a u b 20 V V c u v d u v V

The future value at 5 interest compounded continuously for 7 years of the continuous income stream with rate of 0 02t flow f t 2 100e is 16 491 Compute the interest earned Type an integer or a decimal

Match each function with its graph Function f x f x f x Graph Color a blue b green c red

Take the log In of both sides Simplify using Log Laws Take the derivative implicitly dy Solve for y dx ples Cor 1x 1 2

h x ln xe 2x

A company manufactures downhill skis It has fixed costs of 26 000 and a marginal cost given by C x 1 0 05x where C x is the total cost at an output of x pairs of skis Use a table of integrals to find the cost function C x and determine the production level to the nearest unit that produces a cost of 150 000 What is the cost to the nearest dollar for a production level of 850 pairs of skis Click the icon to view a brief table of integrals C x Simplify your answer Ilse inteners www fractions for any numbers in the expression

f x 8 6 X SY 8 61 4 2 2 4 19 8 6 8 x

Graph each function 32 f x fool 4 2 x 3 2 6 2 2 6 y 4 00 X

2 Use implicit differentiation to find an equation of the tangent line to the curve at the given point M X X J sin 3x xcos 3y 7 y 36 A 9

For the rectangular coordinates 3 1 a plot the point and b give two pairs of polar coordinates for the point where 0 0 360 a Choose the correct plot of 3 1 below A B Ay Ay C Ay OD Ay Q b Give two pairs of polar coordinates for the point where 0 0 360 Type an ordered pair Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Type your answer in degrees Do not include the degree symbol in your answer Use a comma to separate answers as needed

calculator a Choose the graph that represents the point A polar coo1 hates plot the point Give two other pairs of polar coordinates for the point Do not use a R 2 3x 2 2 3x 2 0 OC x 2 3x 2 b What are the coordinates of the point for which r 0 and 2 0 4x O D x 2 3x 2 Type an ordered pair Simplify your answer Type an exact answer using it as needed Use integers or fractions for any numbers in the expression

For the point 1 and c give the rectangular coordinates of the point 3x 4 x 2 3x a Choose the graph that represents the point 1 4 OA 3x 2 in polar coordinates a plot the point b give two other pairs of polar coordinates for the po B x 2 3x 2 Q O C x 2 3x 2 Q G O D x 2 3x 2 Q L b What are the coordinates of the point for which r 0 and 2n 0 4x Type an ordered pair Simplify your answer Type an exact answer using as needed Use integers or fractions for any numbers in the expression

fopl fit x 2 42 of t 2 X

11 In the following diagram OA a OB b and OC c Points P Q R and S are the mid points o OA AB BC and CO respectively Determine the following vectors in terms of a b and c a P A S b B R a PQ b QR

7 Given a 6cm b 3cm and the angle between these vectors when arranged tail to tail is 35 determine 2a b geometrically as well as the angle formed between 2a b and vector a

3 cos vcos 3v sin vsin 3v

7 cos 3vcos 5v sin 3vsin 5v

8 sin 3vcos v cos 3vsin v

Divide Write your answer in fraction form 21 5x 11x 9 x 1

4 cos 6xcos 2x sin 6xsin 2x

An individual needs a daily supplement of at least 385 units of vitamin C and 240 of vitamin E and agrees to obtain this supplement by eating two foods I and II Each ounce of food 1 contains 70 units of vitamin C and 15 units of vitamin E while each ounce of food II contains 35 units of vitamin C and also 30 units of vitamin E The total supplement of these two foods must be at most 30 ounces Unfortunately food I contains 31 units of cholesterol per ounce and food II contains 25 units of cholesterol per ounce Find the appropriate amounts of the two food supplements so that cholesterol is minimized Find the minimum amount of cholesterol amount of food I oz amount of food II 02 minimum cholesterol units

Use a table of integrals to find the consumers surplus at a price level of p 20 for the following price demand equation 14 000 40x p D x 400 x Click the icon to view a brief table of integrals The consumers surplus is 1 Round to the nearest dollar as needed

6 cos 50cos 20 sin 50sin 20

24 4x 20x 5 x 5

18 f x 3x 15

The following graph shows the average candy Consumption of a town in thousands of pounds per year n selected years Estimate the total candy consumption from 2001 to 2006 using rectangles of width 1 year and height determined by the value of the function at the left endpoint Pounds of candy consumed in thousands 0 2000 2002 2004 2006 2008 2010 Year Q The approximate total candy consumption of th town from 2001 to 2006 was thousand pour of candy Simplify your answer Type a whole number

the complex number in trigonometric form where r is exact and 0 0 2 Select the correct choice below and if necessary fill in the answer boxes to complete your choice Simplify your answer Type an integer or a simplified fraction Type any angle measures in radians OA 7 sin i cos OB 7 cos C 7 OD 7 cos sin M i sin i sin ww i cos

Given u and 7 draw the following vectors 4 a u b 20 V V c u v 15 v d u v V v

An amusement company maintains records for each video game it installs in an arcade Suppose that C t and R t represent the total accumulated costs and revenues in thousands of dollars respectively t years after a particular game has been installed and the derivatives C t and R t are the following functions C t 5 and R t 8e 0 1t Find the area between the graphs of C and R over the interval on the t axis from 0 to the useful life of the game and interpret the results What is the useful life of the game years Round to the nearest tenth as needed SILB

A car leasing firm must decide how much to charge for maintenance on the cars it leases After careful study the firm determines that the rate of maintenance M x on a new car will be approximately M x 42 1 x dollars per yea where x is the number of years the car has been in use What total maintenance cost can the company expect for a 2 year lease Whaf minimum amount should be added to the monthly lease payments to pay for maintenance on a 2 year lease Write a definite integral to find the total maintenance cost for a 2 year lease 10x dx The total maintenance cost the company can expect on a 2 year lease is Round to the nearest cent as needed The minimum amount that should be added to the monthly lease payments is Round to the nearest cent as needed

Write the complex number 4 4 3i in trigonometric form where r is exact and 0 0 2 Select the correct choice below and fill in the answer boxes to complete your choice Simplify your answer Use integers or fractions for any numbers in the expression Type any angle measures in radians Type exact answers using as needed OA 4 4 3i sin i cos OB 4 4 3i COS isin

2 For the vectors 3 12 0 and b 5 5 7 determine the vector 2a 5b 3 For the point P 2 4 5 plot this point in R and list the coordinates of the points that form a rectangular prism with this point and the origin Y 2

r 10 csc 0 Choose the rectangular equation that is equivalent to r 10 csc 0 A y 10 OB C x 10 D y 10x 10y Choose the correct graph of the equation below O A B Q 5 O C Q OD 46

r 8 sin 0 is equivalent to what rectangular equation OA x y 4 OC x 8 y 8 www OB x 4 y 4 OD x y 4 4