The limit represents a derivative f'(a). Determine f(x) and a. 8h lim h - 1 h→0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) f(x) = a =

Q: 1 3. (x+1)(x²+4)² dx

A: The given integral is  1/[(x+1)(x2+4)2].

Q: 1) Evaluate the integral dy dx using polar coordinate

A: Explanation of the answer is as follows

Q: (V3, 1,0) and v = (1,0, v/2) is The acute angle between the vectors u = a) O b) A O d) None of these…

A: Given problem:- The acute angle between the vectors u = (√3, 1, 0) and v = (1, 0, √2)

Q: 200 D(r)

A: answer is in next step

Q: Solve triangle ABC if ZA = a = 37.1°, b = 11.5 ft, and c = 13.6 ft. Using the Law of Cosines, ft.…

A: Using law of cosines;a2=b2+c2-2bc cosαa2=11.52+13.62-2(11.5*13.6)cos37.1a2=67.72575a=8.229a ~ 8.23…

Q: A Norman window is constructed by adjoining a semicircle to the top of a rectangular window, as…

A: Perimeter of Norman window(P)=Perimeter of rectangle(P1)+Perimeter of…

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Q: O In 17 lo 6

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Q: The line of intersection of the planes 2x +y - z= 4 and 4x – y+3z = 2 has equation %3D O a) (x, y,…

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Q: Calculate the total area of the glass needed for a KLEEMANN curved building design with a function…

A: we have to find area.

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: 1. Suppose a body has a force of 3 pounds acting on it from the west, 4 pounds acting on it from the…

A: Using vector addition  we determine the force

Q: Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in…

A: Consider

Q: A tangent line to the curve c(t) - (- 4t - 5t + 2, t - 15t - 1) has slope 3 at the pointias) 2-1…

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Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

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Q: (х - 1)(х - 4) 38. у- (х - 2х - 3)

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Q: 3 sin-xe 5%

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Q: Let f be a function defined by f(x) = In(2x2 + 1) and let g be a function defined by g(x) = 2x4 –…

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Q: Region is bounded by y=x y=x2 Rotate about x=2. Find the area. Please help

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Q: Evaluate: S Vx(x – 5)dx

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Q: x²y' + 2xy – 2y = 0

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Q: Find the area under the curve y = 6x° over the interval [0, 2]|

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Q: Frod the averuge vearlue of the durndkam f over Shoe lad eraual [q,9]

A: Solve it

Q: 16) Find the radius of convergance, Rof Ene.series R=? 90x

A: The given series,        ∑n=1∞9nn2xn

Q: Eveluete Khe definde lategal 3 In C) doc

A: To evaluate the integral.

Q: The continuous function g is negative and has domain x > 0. If the asymptotes of the graph of g are…

A:

Q: On the region x2 + y° 0, y > 0, the function f(x, y) = xy has O a) its absolute maximum of 6/3 and…

A: To find the absolute maximum  and absolute minimum of the function f(x,y) in the given region.

Q: x cos y + sin 2y = xy

A:

Q: Find the exact length of the polar curve. r = 6 sin ?,    0 ≤ ? ≤ ?/3

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Q: Let g be a function with derivative given by x2 - 2x - 8 g'(x) = V2x³ +5 - 1<x <5 %3D . At which…

A: Occours

Q: Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area x?…

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Q: Using the substitution u = x + 1 / Væ +1 dæ is equivalent to 1 u +1 -1/2 du /2 1/2 du (4 – 1) /…

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Q: Use Newton's method to approximate the solution to the equation 4 = x+ 2. Use xo = -1 as your…

A: This question can be solved using the concept of methods of approximation of roots.

Q: Scot(x)dx

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Q: Show that the limit does not exist. xy? - 1 lim (Ky)→(1,1) y-1

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Q: y varies inversely as the fourth root of x and when x = 81, y = 10. What would be y when x-45. Round…

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Q: If the marginal profit is P'(x)=x^3-2x+100 and the profit for selling 10 items is $2000, determine…

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Q: Use the divergence theorem to find the outward flux of F across the boundary of the region D. F=…

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Q: IV. Problem Solving: A. Write the expression as a single Integral. Choose your answer from the box.…

A: The given integral,∫02fxdx+∫23fxdx

Q: dy 3. Find of the following equations: dx b. xy = 2x?y – 8x

A:

Q: 21. If F(x)= [ VP +1 dr, then F'(2) = %3D (A) -3 (В) -2 (C) 2 (D) 3 (E) 18

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Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

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Q: To find the distance across a small lake, a surveyor has taken the measurements shown in the figure…

A: The Cosine rule; a2=b2+c2-2bccosAb2=a2+c2-2accosBc2=b2+a2-2abcosC Given; a=850 ft, b=960 ft, C=75°

Q: Consider the definite integral V11 dæ. - 2x -3 The most appropriate substitution to simplify this…

A: Solving

Q: Here are three functions that are related to each other. Correcti Tries: 3 One is f(x). Another is…

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Q: 3. 2. 1 15. The graph of f is shown in the figure above. If , f(x)dx=2.3 and F'(x)= f(x), then F(3)-…

A: ∫13f(x)dx=2.3 and F'(x)=f(x)

Q: Based on census data, the population of Freedonia is modeled by the function P(t) = 309t + 37559…

A: Given query is to find the year when rate of change of population is 1236 people per year.

Q: Consider the diagram shown below. Suppose that O = (0, 0) and A = (3.5, 0) and B = (2.91, 1.95). The…

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