Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² + x + 1, [0, 1].

Q: The first derivative of y = cos(3x-8) is O a. - sin( 3x-8) O b. 3 sin( 3x-8) O. - 3xsin( 3x-8) O d.…

A: Given function is, y=cos3x-8.   It is differentiated as follows: dydx=ddxcos3x-8

Q: 1. find the linear approximation tof (x) at x = xo. Use the linear approximation to estimate the…

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Q: Find f"(x) for the function f (x): = x cOS X

A: The given function is fx=xcosxTo find f''(x)

Q: Find the derivative of y with respect to x. y = cos1 (5x2 + 4) 10x + (5x2 + 4)2 -10x Vi- (5x2 + 4)?…

A: The given function is  y= cos-1(5x2+4)  We have to find the derivative of this function w.r.t. x

Q: The 2nd derivative of the given functions is y = 3 cos (4x – 5)

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Q: Which of the following pair of functions is linearly independent? (a) e, e(*-3) (b) 4, sin2x+ cos2x…

A: Which of the following pair of functions is linearly independent?

Q: The first derivative of y = sin( 4x + 3) is %3D а. - 4 cos(4x +3) b. 4 cos(4x +3) С. cos(4x+3) d. -…

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Q: Find a0 of the function f(x) = sin(x/2

A: Given function is:  fx=sinx2

Q: y = (cos x)* 4. Differentiate the function

A: Given :  The function  y = ( cos x ) x    To find :  The derivative of   y = ( cos x ) x

Q: Find f if f"(t) = 2et + 3 sin(t), f(0) = -10, ƒ(π) = −8.

A: To find f if f''t=2et+3 sint, f0=-10, fπ=-8.

Q: Find the derivative of the function. y = a 3 + cos 3 x)

A: Given: y=a3+cos3x

Q: b)Find the derivative of the function x cos (2x + 3y) = y sin x

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Q: B) Find (w). For the following functions: xue-sinxux(u-¹ + wv) (1) y=- (2) wp-v²

A: Given the function is y=x-2ue-sinxu-x3(u-1+wu)wv-v2. We have to find the values of ∂y∂x, ∂y∂u, ∂y∂w…

Q: Q. 3. a) Find first and second derivatives of the following functions: +7x y=cot(3t-1) 201

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Q: Find the derivative of the functions below: (Choose Four Only) y = (1+ 3x)(3 – x) y = 13x2 – 52x sin…

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