Find the x-coordinate of the centroid of the area bounded by y(x² - 4) = 1, y = 0, x = 4, and x = (Round the answer to four decimal places.)

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A: According to the ε-δ definition of limits says that the limit of f(x) at x=c is L if for any ε>0…

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A: Solution is given below:

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A: To find the equation of polynomial from the graph

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A: Finding f'(x)

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Q: / dw W8 W8

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A: Given problem:- At what points on the given curve x = 2t3 , y = 2 + 10t - 14t2 does the tangent line…

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Q: 1. Use the substitution method to evaluate x² S. VAI ³ + 50° dx

A: Here we have to find the integral using substitution method.

Q: We are trying to prove the following limit. Suppose that we have found a value of such that e =…

A: Given: limx→7 (2x-7)=7

Q: sin x +∞0 Σ n=0 (-1)" (2n + 1)! px?nts] for all x € R

A: Ans: 0.099999983 Solution is attached below.

Q: 10. Use the Comparison Test or Limit Comparison Test to determine whether k=2 k3 k5+2k + 23…

A: The given series ∑k=2∞k3k5+2k+23

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Q: 3. Determine the value of a so that the 2 average rate of change on the function h(x) = x² + 3x + 2…

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Q: 6. Find y" give y = 7³x a) 21³x In(7) b) 63³x In(3) c) 3(7³x)ln(3) d) 9(7³x)(ln7)

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Q: If 3x² + 5x + xy = 1 and y(1) = -7, find y'(1) by implicit differentiation.

A: We can find the answer as below.

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A: We will find the integral.

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Q: What value(s) of 8 are an appropriate choice when proving the following limit? lim (√6x +30) = 0…

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Q: in open rectangular box (no top) with volume 8 cubic meters has a square base. Express the surface…

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Q: Evaluate the integral: dw J 2000 5 W8 W8

A: I have stated the used formulas in the solution

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A: We have to find the slope of the tangent line to the polar curve  r = cosθ3 at the point θ=π.

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Q: gral Izyds xy ds ere C is the spiral r = e from 0 to 0 = 2π. =

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Q: 9. Estimate the value of the convergent series 8 k=1 (-1)^² k! + 2k with an absolute error less than…

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Q: 1. Solve for y3 using the method of successive approximation. dy dx = x+y; y(1) = 1

A: Given Data,y1 = 1dydx = x + y

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A: Let's find total distance traveled by the ball.

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Q: Find the Consumer's Surplus corresponding to q=900 units. (Do no rounding of results until the very…

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Q: Find the Fourier series of the function f on the given interval. f(x) = {0 -2< x < 0, 1 0 <= x < 2}…

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Q: Find dw/dt using the appropriate Chain Rule. w = x² + y² x = 3t, y = 8t (No Response) dw dt

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Q: 7 If f(x) = x² + 10x and g(x) = - X find f(x) · g(x).

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A: Here we have to find the function.