Question 3.1: Let G : <(1)=2+2e“, 0sIs 2n and C, : :(1) =i+e“, 0sisTY (a) Draw the path C, and C2. dz and (ii) dz (b) Calculate (i) --2 : (z-i)'

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A: Given function is Differentiating partially with repect to y, we get

Q: Find the power function f(x)= cx^k such that f(1) = 2 and f(2)=64

A: Given f(x) = cxk and we have to find the values for c and k.

Q: Sketch c(t) = (t^2 − 4t, 9 − t^2) for −4 ≤ t ≤ 10

A: Given c(t)=(t2-4t, 9-t2)    ; -4≤t≤10

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A: given F(t) = e^2t - 8/ 1-t

Q: Differentiate the function f(t) = t^3 − it^2 when t = 2

A: Here, f(t)=t3-it2⇒f'(t)=3t2-i(2t)⇒f'(t)=3t2-2ti

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A: Answer

Q: Differentiate the function. h(t) = √t-8e* h'(t)

A:

Q: Find the average rate of change of the function f(x)=x^3over the interval [1,1+h]. Simplify your…

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Q: Let f(x)=2x^2−4x+14.Findwhere f(x)>0.

A:

Q: the answer that was given was y(t)=Ce^-t + Dte^-t +3t^2e^-t but its wrong I'm looking for the error…

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Q: Now, differentiate the function y' = 4x(1 + 2 In). y" = 4 + 8 + In + 8 In

A:

Q: Differentiate the given function 1)f(x)=1/4x^8-1/2x^6-x+2 2) y=1/t+1/t^2-1/sqrt(t)…

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Q: Find the function f that satisfies f '(x) = 3x^2- 8x+ 2 and f(1) = 6.

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Q: f"(z) = 2r +2 and f'(-2) = -l and f(-2) = 4. Find f'(x) = x^2+2x-1 and find f(4) = = 266/3

A: