13) Let f(x) = 4+4x x Compute f(x), f'(x), f'(x), f'''(x), f(iv) (x), f(v) (x) S f(), f'(), f), F" (), Fam داد We see that the first term does not fit a pattern, but we also see that f(k) (1) = 127 for k>1. Hence we see that the Taylor Series for f centered at I is given by [27 f(x) = 8+ 2/² (x-1) k K=1 6-X 10

Q: For each of the above functions, prove that f(f-1(x)) = f-1(f(x)) = f(x) = +6 f(x) = x3 + 2 f(x)…

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Q: differentiate the question 1 to 5

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Q: Let F(z) = f(f(2)) and G(r) = (F(x))'. You also know that f(3) = 12, f(12) = 3, f'(12) = 5, f'(3) =…

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Q: f(x) = -9 f'(x) = -(x²+9) (x²-9)2 f"(x) = 2x(x²+27) (x²–9)3 4. Given a) Provide a complete analysis…

A: a)

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: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(5) = 6, ƒ(6) = 2, ƒ'(6) = 6, ƒ'(5) = 12…

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Q: A table of values for f, g, f', and g' is given. g(x) 2 8 2 Xx 1 2 3 f(x) 3 1 7 (a) If h(x) =…

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Q: 9. From "First Principles" show that if f(x)= == 2 x²-3' then f'(x) = - 2x (x² - 3)²

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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: C Chain Rule 7) f (x )> (2x +5)

A: To determine the derivative using chain rule.

Q: f(x) then: f'(x) = f'(1) -

A: We are asked to find the derivatives of the function.

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that ƒ(8) = 11, ƒ(11) = 2, ƒ'(11) = 5, ƒ'(8) =…

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Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

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Q: B) If fx) =-3x² +13 and g(x) =x'+8r-2; find the following. i) (g+f)(x) ii) Ax) - glr) C) 1) If f(x)…

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Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that aª Then F'(a): = = = 8, f(a) = 2, ƒ'(a) =…

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Q: Let F(x) = f(f(xæ)) and G(x) = (F(x))² . You also know that f(9) = 3, f(3) = 2, f'(3) = 5, f'(9) =…

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Q: Let F(x) = f(x) and G(x) = (f(x))³. You also know that a = 3, ƒ(a) = 3, ƒ'(a) = 11, f'(a³) = 9 Then…

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Q: 3) a) Find the real and imaginary parts of the following functions: ^) f(2)= ²² +₁ Z-1 2) f(z) = 3z²…

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Q: 8. What is the multiple zero and multiplicity of f(x) = x + 10x + 25x? multiple zero = -5;…

A: To write the multiple zero and multiplicity

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

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Q: 1) (a) If f is one-to-one and f(-15) = 2, then f '(2) : and (f(-15)) is one-to-one and g(3) 7, then…

A: Given function f is one-to-one so f has only one image in the range in other words there will not be…

Q: 5 14) f(x) = (2х - 3)4 40

A: Given,             fx=52x-34

Q: which one is y=g(x), y =g'(x), y=g''(x), y=g'''(x)

A: We have to fund which graph corresponds to g(x),g'(x),g''(x),g'''(x)