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.

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

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A: Given f'( x ) = 2x

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A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

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

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Q: Composites of Functions

A: As per company guidelines, I can solve only first three subpart.

Q: For any function, With utilization of the product rule for functions of one variable (eq1), show /…

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

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

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Q: Let F(2) = 2, F'(2) = 3, H(2) = 4, H'(2) = 3. A. If G(z) = F(z)*H(z), then G'(2) = _______ B. If…

A: The Product Rule:The Quotient Rule:

Q: 4.* (a) Let S = {1, 2, 3, 4}. Define F: SN by F(x) = x² for each x = S. What is the range of the…

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Q: Suppose f(x) and g(x) are two functions such that: • f(3)=1 • g(3)=1 • f(3)=5 • g'(3)=7 What is…

A: we know that uv' = u'v+v'u                   product chain rule of differentiation

Q: Let f(x) = Vx and g(x) = x³ +1. Find 29 a) f(g(2)) b) g(f(4)) c) f(F(16)) d) g(g(0)) e) f(2+ h) f)…

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Q: Let g be an analytic function with g(-i) # 0, g3) (-i) = -12, and g(4) (-i) = -36. _g(z) If f(z) =…

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Q: Let f(x) ƒ'(x) = ƒ'(3) = = √2x² + 4x + 3

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Q: Compute f(5) (e) forthe function f(x) = x³.In(x+)

A: f(x)=x3.ln(x4)f(x)=4x3ln(x)Differentiatef'(x)=4x2+3x2ln(x)f'(x)=4x2+12x2ln(x)Differentiatef''(x)=8x+…

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

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Q: 18) Suppose that f is continuous and that A) -7 B)-14 Find the area of the shaded region. 19) (0,0)…

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

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