Calculus Questions

Consider a function h that is continuous over 10 10 and let 10 foto h 0 Use the above information to evaluate each of the following definite integrals 17 forth he 7 h x 7 dx 10 h x 7 dx Assuming h is odd Assuming h is even 10 10 h x dx h x dx 5 10 h x dx

Consider the graph of f n 1 2 3 4 5 6 7 1 fl S f f x dx The shaded region over 0 2 has an area of 9 and following definite integrals f x dx f z dz 9 Q 0 1 pt 30 f x da 171 Use this information to evaluate th

Let If Use the given definite integrals above to evaluate each definite integral below 7 3f v dv 7 f v 6 du f v dv f v dv f v dv 108 f v dv 108

Find the rate of change of total revenue cost and profit with respect to time Assume that R x and C x are in dollars R x 40x 0 5x C x 4x 20 when x 35 and dx dt 25 units per day The rate of change of total revenue is The rate of change of total cost is The rate of change of total profit is per day per day per day

circle is growing its radius increasing by 2 mm per second Find the rate at which the area is changing at the moment when the radius is 26 mm When the radius is 26 mm the area is changing at approximately Round to the nearest thousandth as needed second s mm mm per second second s per mm

dy Differentiate implicitly to find Then find the slope of the curve at the given point dx 6x 7y 157 5 1 dy dx The slope of the curve at 5 1 is 11

Suppose that x and y are related by the equation 5x 4y 2 and use implicit differentiation to determine dx

Suppose that the price p in dollars and the number of sales x of a certain item are related by 4p 4x 2px 72 If p and x are both functions of time measured in days Find the rate at which x is Changing when x 3 p 6 and dp dt 1 1 The rate at which x is changing is Round to the nearest hundredth as ne day s per sale day s sale s sale s per day

uppose that x and y are related by the given equation and use implicit differentiation to determine x y y x 6 dy dx dy dx

Consider the function f x 7 defined on 7 7 a Compute the left Riemann sum L10 L1o help numbers b Compute the right Riemann sum R10 R10 help numbers c Compute the average value of L10 and R10 Average value he help numbers d Compute the area under the graph of f Area help numbers e Compare the two values found in c and d The average value is the area

Suppose f x 14 H a The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f x on the interval 4 x 6 The value of this left endpoint Riemann sum is and it is an the area of the region enclosed by y f z the x axis and the vertical lines 4 and 6 b The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f x on the interval 4 6 The value of this right endpoint Riemann sum is and it is an the area of the region enclosed by y f x the x axis and the vertical lines 4 and 6 Left endpoint Riemann sum Right endpoint Riemann sum

Suppose f x 7 10 a The rectangles in the graph on the left illustrate a left endpoint Riemann sum for f x on the interval 4 6 The value of this left endpoint Riemann sum is and it is an of the region enclosed by y f x the z axis and the vertical lines 4 and x 6 the area b The rectangles in the graph on the right illustrate a right endpoint Riemann sum for f x on the interval 4 6 The value of this right endpoint Riemann sum is and it is an area of the region enclosed by y y the c axis and the vertical lines and v the Left endpoint Riemann sum Right endpoint Riemann sum

Given the function f x x using 5 rectangles of equal width find an approximation to the area between the curve and the x axis over the interval 3 9 if the heights of the rectangles are found by evaluating the function at the left endpoints right endpoints and midpoints of each subinterval created by a partition of the interval given Using left endpoints the approximate area is Using right endpoints the approximate area is Using midpoints the approximate area is

Consider the function f x 100 x 10 defined on 0 10 a Compute the left Riemann sum L6 L6 help numbers b Compute the right Riemann sum R6 R6 help numbers c Compare the two values found in a and b The left Riemann sum is the right Riemann sum

Estimate the areas under the curve by computing the left Riemann sum L2 F1 16 1 8 1 0

1 Find a power series representation and interval of convergence for the derivative of 1 8 x f x

Given the function f 2 compute the left endpoint Riemann sum using m 6 on the interval 1 11 Ls help numbers

Find all points where the partial derivatives of f x y are both 0 where f x y x 12x y 27y Number of point s where the partial derivatives of f x y are both 0 Choose one

rt 2 of 2 Ints eBook Hint Print References 1 Prepare journal entries dated June 30 to record a raw materials purchases b direct materials used c indirect materials used d direct labor used e indirect labor used f other actual overhead costs and g overhead applied View transaction list Journal entry worksheet 1 2 3 Transaction Note Enter debits before credits 4 5 Record the purchase of raw materials on account 6 General Journal 7

The floor of a rectangular bedroom requires 288 ft of carpeting Molding is placed around the base of the floor except at two 3 ft doorways If 62 ft of molding is required around the base of the floor determine the dimensions of the floor 3 ft The floor is ft hy 3 ft ft

COS Tk

Evaluate the integral 14 A dt N B C G 13 D

Find the partial derivatives fa and fy of the function f x y The variables are restricted to a domain on which the function is defined f x y 5x 3xy 3y fr x y 5x 3y 3y fy x y 5x 3x 9y X X

Find the partial fraction decomposition 2x 21x 21x 75x 96 2 x 8x 16 X 3 X

Given the functions f x x 6x g x 6x h x 5x 6 Evaluate the function h g x for x 6 Give your answer in exact form h g 6 is Undefined

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

Set up the form for the partial fraction decomposition Do not solve for A B C and so on 12t 8 2t 9t 18 00

A water main is to be constructed with a 25 grade in the north direction and a 10 grade in the east direction Determine the angle 0 required in the water main for the turn from north to east D 0 75 5 radians Type your answer in radians Round to the nearest hundredth as needed North East not drawn to scale

0 A 45 X y 2 9 3 B 27 9 3 C 36 D 18

6 3 Sx d A 1

5 Show that f x 2 e is an even function Sketch fand describe its symmetry 10 9 8 10

y t 7 t 1 y 2 In 1 t t 3 y 1 4 Sorry we can t solve this one just yet Determine largest interval astch on which the

2y 2 y X dy 2y x 0 x 0 dx

Find the exact solutions of the equation in the interval 0 2 sin 2x cos x 0 X X X X X X X smallest value largest value

Use the figure and trigonometric identities to find the exact value of the trigonometric function below in two ways a 4 cos a sin B 4 cos a sin B 4 cos a sin B 4 V 12 2 2 B

a 5 13 b 12 13 c 5 12 sin 8 cos 8 tan 0 d cos 20 e tan 20 5 0 12

Begin with the graph of y e and use transformations to graph the function f x e Determine its domain range and horizontal asymptote What is the domain of f x e The domain of f x is Type your answer in interval notation What is the range of f x ex 37 The range of f x is Type your answer in interval notation What is the horizontal asymptote of f x x 3 4 10 8 6 4 2 10 8 6 4 2 2 4 2 6 8 40 8 11

dy 2 dt y t y 0 1 Aproximate yhe solution of IVP at t 1 by eu mothod b 05

3 Find the missing side lengths Leave your answers as radicals in simplest form 2 1 C x A x B x D x 5 n A m B m 30 C m 10 30 2 40 15 3 20 3 y 3 5 6 3 20 3 3 m 5 3 2 y 15 D m n 2 n 5 n 2 y 10 3 3 5 5 3 5 n 2 4 4 5 2 10 3 3 40 3 5 6 3 4 u 5 2 45 V A u 3 v B u 2 3 3 C u v 3 60 2 B a 3 2 3 a N W D u 3 v 2 V b A a 5 b 5 5 2 2 32 3 3 2 2 b 5 5 C a b 2 2 D a 10 b 10 5 2 2

y p t y q t y 0

206 986 zimsb nA CA TC shoitanut sint b Find Sex sec X fanx dx tosini stinitabal Pa Lidel 0 Hint Table 4 9 PP325 see the title page

t t 1 y 1 t 1 y 0 t 1 Solution of this ODE on interval 1 infinite is n y1 t e t Find another solution y2 so y1 y

dy dt sin 2y t 1 cos y 2 t 1 y 0 TT O 6

Use the Law of Sines to solve the triangle Let b 54 7 yd Round your answers for a and c to two decimal places C x X yd X yd am C 88 352 22 45 a

A water main is to be constructed with a 25 grade in the north direction and a 10 grade in the east direction Determine the angle 0 required in the water main for the turn from north to east 0 radians Type your answer in radians Round to the nearest hundredth as needed CLB North East not drawn to scale

5 cos x sin x dx

2t y 3y e y 0 a lim t 0 t

Use the Law of Sines to solve the triangle If an answer does not exist enter DNE Round your answers to two decimal places A 119 a 125 b 202 B C C x X X

2 Given a function of g x 2x 8x 3 on 1 5 same as previous problem answer the following questions You cannot use the graphic calculator to find the answers A Use the First Derivative Test to identify the local extreme value of g x when x 2 ve Test to identify the local extreme value of g x when x 2