E[x(t)]=2 and Ryr (7) = 4 + exp (-2 It). Let Y(t) be the voltage across capacitor. Find E[Y(t) and G. ().

Q: Find the function f (x) for which f (x) = e-5x, f (0) = 1.

A: A function is a relation which maps each value in its domain to exactly one value in its range. For…

Q: Given h(x) = (-x² – 2x – 2), find h' (0)-

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Q: i(t) = (A₂ + A₁t)e-at

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Q: Determine h(1) and h'(1). h(x) = [f (x)]2

A: The function h(x) is a composite function since its input is another function f(x). Now h(x)=[f(x)]2…

Q: Let g(x) = x³ – 2x + 6. Find f(x) so that f'(x) = g'(x) and f(1) = 2. NOTE: Enter the exact answer.…

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Q: g(t) = (t – cos t) sin t. Find g'(t). s

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Q: Given the functions fz) = 3* and g(x) = sin x, determine the domain of the combined function y=…

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Q: Show that log, (Vx + Vx – 1) + log.(Vx – Vx – 1) = 0.

A: To show that logax+x-1+logax-x-1=0. Solution: We know that, logm+logn=logmn Simplifying the left…

Q: (c) y = = b √ax² + 1 = e tan(bw) -αω (d) H (w):

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Q: *(x) = x² +x – 7 , find f'(a) at a = -2 by using the definition of derivative.

A: To find the f'(a) using definition of derivative

Q: Let h(x)=f(g(x)). If f(−4)=−3, f′(−4)=−1, g(1)=−4, and g′(1)=3, find h′(1).

A: The formula one have to use here is f(g(x))'=f'(g(x))* g'(x)

Q: = f(x) = (4x – 2)(x² – 3). F %3D

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Q: Find f′′(0) if f(x) = sinh−1(π2 + x2).

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Q: Let a + 0 be a constant. Give an example of a function y = f(x) for which ay – y' = 0 and g?y – y" =…

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Q: Given f(x) = -3x + 3 and x = 3r In (2s). Find f, (2, 4). Give your answer correct to two decimal plo

A: Follow the procedure given below.

Q: kt Convert the equation f(t) = 310(1.13)' to the form f(t) =

A: answer is in next step

Q: Find the function f(x) such that  f ′(x) = f(x)(1 − f(x)) and f(0) = 1/5.

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Q: Determine what functions of time will appear in y(t). Which y(t) are oscillatory? Which have a…

A: The given function Ys=2ss2+4s+8. We have to find the function yt, and yt are oscillatory, and a…

Q: Find

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Q: Let y=y(x)=2(√x)⋅f(x) and suppose f(4)=2, f′(4)=-2, find y'(4)

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Q: a.) If     f(x) dx   = 4x9 − 8x6 + C, find f(x). f(x) =

A: Given: ∫fxdx=4x9-8x6+c                                          ..1 for finding fx, we differentiate…

Q: Find y as a function of a if y(1) = −2, y′(1) : = 4. y = x²y" + 9xy' + 16y = = x³,

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Q: Let f(u)=u4 and g(x)=u=3x3+1. Find (f◦g)′(−1).

A: We have to find out

Q: functions identical?

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Q: Let g'(x) 0. B. g(1) = - 3, g(7) = 1, g(15) = 10 1 C. g(1) = 1, g(7) = 7, g(15) = 14 D. g(1) = 10,…

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Q: Find y as a function of tif y(3) = 8, y'(3) — 9. Y - 49y"+126y + 85y = 0,

A: Find  as a function of  if  ,  .

Q: Find f. f ″(x) = 20x3 + 12x2 + 8,    f(0) = 6,    f(1) = 3 f(x) =

A: To solve the following