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Q: Question 3 > Use part I of the Fundamental Theorem of Calculus to find the derivative of 14 dt f'(x)…

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A: Here we have the perimeter of the isosceles triangle = 38 m,  Let the equal sides of triangle = x…

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Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

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A: Given query is to find the possible value for g(7).

Q: 12 (2). Here is an Ry region, in the XY plane: Consider the change of variable u = xy and v = 3y +…

A: Here we have to write the integral by using change of variable.

Q: 4. Find the divergence and curl of the following vector function: F(x,y, z) = ( arctan(ry),…

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Q: 1 4 5 1 To find the blue shaded area above, we would calculate: 9. f(x)dx = area a Where: a = b =…

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Q: Suppose that F(x) = f(t) dt, where 14) = [" V3 + u° du. %3D Find F" (2). F" (2) =

A: We have to find the value of F"(2).

Q: If u(t) = (sin(2t), cos(5t), t) and v(t) = (t, cos(5t), sin(2t)), use Formula 4 of this theorem to…

A: We will find the dot product.

Q: 2e Evaluate the integral dx 2x +3

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Q: Given the force fieid F, find the work required to move an object on the oriented curve. F= (y, z,…

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Q: d²u A particular solution of the differential equation du - 2u=3e2t – 18e-tis dt? dt Select the…

A: Particular solution

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Q: Suppose that f(x)=2x^−4+5x^−2 Evaluate each of the following: 1. F' (2)= 2. F' (-1)=

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A: Here we have to find the general term.

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A: We can solve this as follows:

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A: continously compounded formula:A =P er tA=final amountP=Principal amountr=ratet=time (in…

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Q: 1)2xsin-13x

A: Given     write

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A: The detailed solution is given below  Thank you

Q: 1. Let f(x) = - sin(2x) and g(x) = cos(x). %3D (a) Find the amplitude and period for f(x) and g(x)…

A: f(x)=-sin(2x)-1≤sin(x)≤1-1≤-sin(2x)≤1Amplitude of f(x) is 1.g(x)=cos(x)-1≤cos(x)≤1Amplitude of g(x)…

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A: Given:

Q: Solve the exponential equation algebraically. Approximate the result to three decimal places. e2x –…

A: Solving the problem by finding the value of x.

Q: 8. Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere of radius 10…

A: Given problem:- Find the dimensions of the largest-volume cylinder that can be inscribed in a sphere…

Q: Find the length of the curve y = xVa 0 <x < 1.

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Q: x1 x2 x3 x4 x5 x6

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Q: length of the curve r = 4 sin 20 for ÷sos 6 2

A: To find the length of the curve r=4 sin 2θ for π6≤θ≤π2.

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Q: The population P of a bacteria culture is modeled by P = 4100e“, where t is the time in hours. If…

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Q: n(x-3)" Find the series' radius and interval of convergence Zn=1 2n /n2+1 100 Paragraph B IU A Lato…

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Q: 3. Find the derivative of each of the following functions. Justify your answer. I sin z (a) f(x) =…

A: As we know that; The Product rule: f·g'=f'·g+f·g' The Chain rule: fgx'=f'gx·g'x   And…

Q: (a) 12t – 5t? + 9 dt = +C. (b) u714 TA + 4.5ū du = +C. dx = 5x6 (c) +C.

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Q: When evaluating the following integral 16dr using trigonometric substitution, Part A The correct…

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A: Series

Q: Question * Suppose X, Y are two discrete random variables with probability function given by: Y \ X…

A: Given

Q: (a) At what point do the curves ri = (-4+t, -6 – 2t, 7+ 2t + t2) and r2 = (-5 – 2s, -4 +3s, 6 + s?)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: POS jma- 3 d 1 sin t dt %3| dx 1 1 (A) – x sin(x²) (B) sin(x²) (C) x sin(x²) (D) –sin(x²) ов O O O O

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Q: Given the functions f(x) = . x + 2 and g(x) = x², determine all values of x for which Ag(x)) =…

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Q: 1. ř (t) = (3 – 4t) i + 6t j- (9 + 2t) from –6 < t<8. %3D

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