Suppose that_F(s) = L{f(t)} exists for s> a ≥ 0. a) Show that if c is a positive constant, then £{f(ct)} = e{f(et)} = ! F[ª] b) Show that £~¹{F(ks)} = = k 1 = c) If a and bare constants with a > 0, then £¹{F(as+b)} : s> ca. bt +18 a

Q: Suppose that f(x) Evaluate each of the following: f'(3) = %3D f'(-1) =

A: Given function is : fx=3x9 The given function can be written as : fx=3x-9

Q: dH f(5) = 8, f' (5) = 4 f(26) = 8, f'(26) = 6, g(5) = 1, g'(5) = -9, and H(x) = f(r² + g(x)). Find…

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Q: It is known that the function f(x)=(x-2)*e^x+a*(x+1)^2 has two zeros. (I) Find the range of values…

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Q: If f(x) = f' (x) for all æ, then f(x) = = f" (x) for all x. True False

A: f(x) = f'(x) for all x Then f(x) = f"(x)  for all x

Q: Let x + 5 f(x) f-'( – 2) = Preview

A: We will find f^-1(x) first. Plug f(x)=y Then switch x and y Then solve for y. Put y=f^-1(x)

Q: Syppese that f(5) =! f'(5)= 5)=-3 g(5)=7 and a) (5)

A: Given:- Suppose that f(5) = 1,f'(5)=4 ,g(5)=-3, g'(5)=7   a) (fg)'(5)   b) (f/g)'(5)   c) (g/f)'(5)

Q: Show that f (−1) = f (1), but that there is no point in (−1, 1) where f (0) is zero. Why does this…

A: Given: fx=1-x2/3 So, f-1=1--12/3=1-1=0 Also, f1=1-12/3=0 Thus, f-1=f1

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that a¹ = 14, ƒ(a) = 3, ƒ'(a) = 8, ƒ' (a³) = 6…

A: Use the following formulae, to obtain the solution. Chain rule for differentiation:…

Q: Suppose that f'(x) = 2x for all x. a) Find f(4) if f(0) = 0. b) Find f(4) if f(2)= -1. c) Find f(4)…

A: Given f'( x ) = 2x

Q: 4 Suppose that f'(x) = 2x for all x a) Find f(5) if f(0) = 0. b) Find f(5) if f(4) = 14. c) Find…

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Q: Suppose that...

A: We are given: f(2) = -3 , g(2) = 4 , f'(2) = - 2  and  g'(2) = 7  Now, based on the given four types…

Q: a) x³ - x f (x) = 2x² + x − 1 - b) f(x) = ax + b cx - d

A: Here we have to evaluate for a) and b) the value of f'(x).

Q: Show that the GHASH function calculates (X1 • H™) Ð (X, · H"-1) © O (Xm-1° H²) O (Xm· H) ...

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

Q: Suppose that f(-4)=3, f'(-4)=0, g(-4)=3, g'(-4) = 4. Use this to compute (f•g)'(-4)

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Q: Let f(x) = 2 – 2², x > 0 f'(x) = Preview

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Q: Suppose that Find f'(2). f'(2) = f(x) = = e³x x² + 4

A: Given f(x)=e3xx2+4   We are required to findf'(2)         The following formulas of derivatives has…

Q: Iff

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Q: (g/f)(x) f(g(x)) g(F(x)) f-1(x)

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: Let h(x) = x³e" k6*. Find dr (h(x)) wherek is a real number (i.e. k is a constant).

A: Given: h(x)=x3ex3-k6x To find: ddxh(x)