Problem 9: In (a)-(e) below, find L{f(t)} or L-'{F(s)}, as appro priate. (a) f(t) = (te' – 1)² (b) f(t) = |2t – 1| – |t – 1| (c) f(t) = cos²(t - }) - 3

Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

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Q: = In (2x) + cos (6x)

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Q: dx -= In(F (x))+C. What is F (/3) if C=0? For (x+x³) (xtan-'(x) + 1)

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Q: (xii) f(t) = 3e'cosh4t (xiii) f(t) = 3e-2"(sinh2t – 2cosh2t)

A: Given :-  The table of Laplace transforms below and any relevant properties used. (xii) f t = 3 et…

Q: Let h(z) tan(5x + 5). Then h' (2) is and h'' (2) is

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Q: Suppose f(x) f'(2) = ex x² +5 . Find:

A: Given: f(x)=exx2+5

Q: 5.f (x) = 2sinx – cosx + tanx

A: We have to find the step by step solution for the problem 5.

Q: 15. If f (x) = (cos(√/z) - In(x2))³, then f'(x) = О А О в О с OD (A) 3(-2;sin(vz) - 2) (B) 3(cos(√z)…

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Q: Suppose that f has an inverse, ƒ(2) = 5, and f'(2) = What is (f~')'(5)? %3D

A: (a) Given that f has an inverse, f(2)=5, and f'(2)=-34 As  f(2)=5 so, f-1(5)=2

Q: 5. Suppose f(3) = -2, g(3) = 5, h(3) = –1, f'(3) = -4, g'(3) = 3, and h'(3) 2. Find the value of the…

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Q: Suppose h (x) = sin(f (g (x))) S(1) = 0 ' (1) = 1 g (1) = 1 g' (1) = 2 Find h' (1)

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Q: 4 given that g(2) = 1 and g'(2) = – 5, what is F'(2)? If F(x) = %3D g(x)' %3D

A: Given, F(x)=4g(x), g(2)=1 and g'(2)=-5We need to find F'(2)

Q: If f(3) = 1, f'(3) = 1, g(3) = 1 and g' (3) = -2, then P dz g(x) I f(z) %3D Answer:

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Q: If f(x) = x cosh then f'(9) = 1 ¹() x²-9

A: The given function is

Q: tanx 7. f(x)= x²-3

A: The function is  f(x)=tanxx2-3

Q: If g(x) = cos(x) then g'(x) = = g'(1) = -sin(x)

A: NOTE: Refresh your page if you can't see any equations. . take derivative…

Q: 5. A function y = sin x is transformed into = -sin (3x) - 4. What is a possible transformation?

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Q: If f(x) = sin(cos(2x)), then find f' O-1 O -2 O 1 ||

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Q: f(2)=-3. f'(2) = 10. g(2)=4, and g'(2) = 1. then evaluate (fg)' at x = 2

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Q: Compute the derivative: tan-'(ax) (bx) (a) y = sin='(x²) (b) y = (tan-1 r)³ (c) y = sin

A: (a)   Differentiate the given equation with respect to x, dydx=ddxsin-1x2=11-x22ddxx2=2x1-x4

Q: If we let f(x) = 1-4x/1+4x What are.... f’(5) = f”(5) = f”’(5) =

A: we have to find derivative at that point

Q: Problem #7 Find f'(x) if Ax) = tan-"(2x² - 4)

A: We differentiating both sides with respect to x and solve it. See 2ndnd step.

Q: 6. (a) e' sinht (b) 3e2 cosh 4t

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Q: 9) Find f(x) if f'(x) = 7 sin x + 2x - 3 and f(0) = -3

A: Obtain f(x) by integrating the given first derivative as follows.

Q: Given f''(x) = 2x – 5, f'( – 3) = 1, and f( – 3) = 2. %3D a) Find f'(x) = b) Find f(2)

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Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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