Find the average value of the function on the interval. Give an exact answer. f(x) =  1/(x-7)^2  with the point 0,6

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A: Area of the region is shaded below.

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Q: cot ve csc² Ve do 3 Vo (4 + cot? Ve)

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Q: Find the centroid of the region R bounded by the graphs of y x and y 1. 1) Which of the following…

A: To find the area of the region R.

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A: Follow the procedure given below.

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A: We have to determine area of bounded

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A:

Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

Q: x arcsec x dx ? xdx A. x Arcsec x - 25- ... B. ** Arcsec x -- V-1 xdx xdx C. x Arcsec x + 25- xdx D.…

A:

Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: Sketch and use a double integral to find the area of the region R bounded by the lines: y = 0, y = x…

A: Graph of the given fucntions

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Q: – (x²- 1) dx using P (1 -;*)-^;* / * m in terms of A?

A: Use simple integration formula.

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: The given function,   f(x)=1x+ln x, 0.6≤x≤5

Q: ) Let R={(x.y): 0sx,Osy, +ys4) be enclosed region. The result of the following double integral (by…

A: Given region R=( x,y) : 0≤x, 0≤y , x2+y2≤4

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A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

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Q: (7) If 4.5* = 97, an approximate value of x is (A)x = log(97) × 1.987 (C) x = In(97) z 4.575 (B)x =…

A: 7.    4.5x=97 Note:      Multiple questions are given, we are answer with only one question. if you…

Q: dx 1- cos 2x

A: The given integral is ∫dx1-cos2x Now,        cos2x =1-2sin2x       ⇒  1-cos2x=  2sin2x…

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A: Use the algebraic substitution and solve the integration.

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Q: |sin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) sin(2x) 12 8 8. + C 4 sin(6x) sin(2x),…

A:

Q: 5) Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If…

A: Note: Rate of change of volume of conical pile is equal to rate of change of sand pouring from the…

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Q: sec (In x)dx

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Q: Evaluate | 4x2 + 4x + 5 dx

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Q: 3x2 + 7x + 28 A f(x) Using partial fraction, evaluate x3 + x2 + 7x dX, the decomposed fraction is x2…

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Q: (6) When David was born, his grandparents deposited $10,000 in a college account that promised 6%…

A: Note: As per company policy we are supposed to solve only 1 question. So, kindly repost other…

Q: 1.) Find the area bounded by the region x = 4y + 4 and y= x+ 2

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Q: S csc6 cot* w dw W

A: Given,           ∫csc614wcot414wdw

Q: 3x2 + 7x + 28 dx x2 + x3 + 7x Using partial fraction, evaluate

A: We know that integration power rule is  Integration of xn is xn+1/n+1.   Here i attached the…

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A: The standard form of the first-order linear differential equation is: dydx+Py=Q Where P & Q is…

Q: 41. Suppose that both f and g have inverses and that h(x) = (f o g)(x) = f(g(x)). Show that h has an…

A: Explanation of the answer is as follows

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Q: x³ + 6x2 + x+2 2 Tan Ve fx-1 ax + In{(x+ 1)*(x² – x + 1)"| + The resulting integral of -X+ -1 + C,…

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Q: dx x2 — 2х — 4

A: I=∫dxx2-2x-4=∫dxx2-2x+1-5=∫dx(x-1)2-52

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A:

Q: Find the indicated derivative. f (x) = (x³ – 5x + 2)(x² + x – 7); find f"(x). %3D

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Q: cos x Given: tan x dx. Using trigonometric transformation , the integral in terms of u is sin x Cos4…

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Q: Using rectangles whose height is given by the value of the function at the midpoint of the…

A: By using rectangles whose height is given by the value of the function at the midpoint of the…

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Q: are

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Q: Which interval of 0-values corresponds to the shaded region in the graph of r = f(0) = 2.1 – 0? On…

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Q: 1) Hs] Solve the IVP: y" – 8y + 16y = 0, y(0) = -3 and y (0) = -1. %3D |

A: Use homogeneous differential equations to find solution.

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Q: Show that the following are equal using set identities. Provide the correct solution with the name…

A: The left side is: C∩C-B∩C∪A∩B-B∩C-A We first simplify inner parts:  C-B∩C A∩B-B∩C