Theorem 11: Let f(t) and g(t) be two functions of class A and let L[f(p);1]= f(t) and L"[E (p);t] = g(t). Then L"[7{p) - g (P};<]= [, f(1)8(t= u)du = f*g.

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

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Q: Prove that if F(s) = L{f(t)} then L{t" f(t)} = (-1)" d"(F(3)) ds

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Q: 7) Use Theorem 7.1.1 (Table) to find L{f(1}} for the following: S)-(e*-e*)}° a.

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Q: Let c =8 If f (x) = ecsin(). Find f' (0)

A: Given c=8and f(x)=ec.sin(x)⇒f(x)=e8sin(x)

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Q: Let Compute f'(2). ƒ(x) = x³ + 3ª

A: This is a problem related to differentiation of the function. Please follow the procedure given…

Q: Let f(x, y) = (- (3z + y))°. Then

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Q: 3 Let f(x)= x³ - 2x+: Calculate by definition f'(1). X

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Q: Let /: X→Y be a function, A, B C X and C, DCY. Show that: 3. If CSD then SF (D) 4. f¹(COD)=f-¹(C)…

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A: Consider the function z=f(x)·g(x) where f and g are both function of x. So we can rewrite the…

Q: Let 11 f(x) = ( – 2a² – 4)(7z² – 4)" - - f'(x) =

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Q: We are given the following functions f : Z → Z × Z, f(x) = (x^2, x^3).  (a) Find images f({1, 2, 3})…

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Q: et f and g be the functions in the table below. f(x) g(x) f '(x) g'(x) 1 2 4 1 3 7 2 1 7 (a) If F(x)…

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Q: uppose that f and g are functions such that f(5)=3, f'(5)=-2, g(5)=4, and g'(5)=-5. nd h'(5) where h…

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Q: Given f(x, y) and y = y(x), we can define a composite functiong(x) = f(x,y(x)).

A: a)Given , gx=fx,yx Then, g'x=∂f∂x+∂f∂yddxyx  [∵y=yx]⇒g'x=∂f∂x+∂f∂yy'x

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: Consider the table of vales for the functions r). J ), u() and g'(x): If the function k is defined…

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Q: 3. If L{F(t)}=f(p) then L{F(at)}= (a) f(2) (b) 음/ (B) (c) af) (d) 금f(ap)

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Q: {6} = I ( (b) T = [4,9) %3D (c) T = [-4,9] -

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Q: Let f(2) = (32² – 7)* ( – 7æ² + 8)² f'(x) =

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