1. Let f : (−1,1) → R, f(x) = (1+x³)-³. Compute g' : (0, 1) → R where (a) g(x) = X X f. (b) g(x) = [*" f ƒ.

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: Let c =3 If f (x) : Cind f! (0

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Q: 4. Let f be the function given by f(x) = 4-x. g is a function with derivative given by g'(x) =…

A: Given f( x ) = 4 - x

Q: QUESTION 7 The y-intercept of f(x) = (x +2)² is QUESTION 8 Given A = 100(3) where A is the number of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let f(x) = 3". As x → 0, what does f(x) → ?

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Q: Consider the functions f(t) = e' and g(t) -81 defined on 0 st<o. %3D = e (a) (f* g)(t) can be…

A: Consider the functions, f(t) = et and g(t) = e-8t

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: 7 x + 2 Let f(x) = x4 . x + 5 f'(x) = %3D

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Q: Suppose that f(a) = f(b) = g(a) = g(b) = 0 and the second derivatives of f and g are continuous on…

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Q: Suppose g and h are everywhere differentiable functions such that g(2) = 1, g' (2) = 2, h(2) h'(2) =…

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Q: X = (1-_-_-_-)* 2 o then f(x) tend:

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Q: Let h(x) = f(g(x)). If: f(3) = 0, f'(42) = –5, f'(3) = 4, g(3) = 42, & gʻ (3) = 0, then h'(3) =

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Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: 6) When some variable z is a function of time (t), the derivative of z with respect to t is denoted…

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Q: 2. If g(x) = (ƒ 03ƒ •4f)(x) = ƒ (3ƒ (4ƒ(x)). Determine gʻ(3), given f(3) = 1, ƒ(4)=1, ƒ'(3) = 2 and…

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Q: 7. Determine where the function is continuous. (a) f(x) = 1+x (b) g(x) = sinx+x² + x + 1. x² (c)…

A: This is a problem related to continuity of thr function. Please follow the procedure given below.

Q: Let g(x) = = X-f(x) S(x) , find g'(1),if f(1) = 4 and f'(1) = 2

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Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: Suppose f(r) = (In z)e. What is f'(x)?

A: d/dx (f(x)g(x))= f(x)g'(x)+g(x)f'(x)

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: 3. Let there be some a, b R such that f(a)ƒ'(a) = f(b)ƒ'(b) + 1. Show that f f(x) f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

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

A: Given, k(x) = f(g(x))