Problem 1 (2 point) Show that if f is continuous and positive function on [0, 1] (i.e., f (x) > 0 for all x E [0, 1]), and if g continuous and strictly positive function on [0, 1] (i.e., g(x) > 0 for all x E [0, 1]), then 1 1/n ( f(æ)"g(x)dx = sup f(x). xɛ[0,1] lim

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A: We the continuity of f to show that f has unique fixed point

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Q: Problem #11: Let f(x) Find f"(In 2) (A) - (B) (C) (D)- (E) (Đ © H) - Problem #11: Select v

A: topic - functions and derivatives    Option H  f(ln2) =-6/343

Q: 1. If the graph of y = f(x) contains the point (0,2), and f(x) > 0 for all x, then f(x) = dx (a)…

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Q: 8. A table of values for (x), g(x),f'(x), and g'(x) has been given. Make sure you show ALL…

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Q: Find values of x, if any, at which the given function is not continuous. (a) f(x) (b) f(x) = |x³ -…

A: Find the x values where the function is not continuous.

Q: Evaluate (f o g)(x) or f[g(x)] f(x) = x² – 3x - g(x) = x + 5 (fo g)(x) = f[g(1)] %3D

A: Given function is : fx=x2-3xgx=x+5 To find the value of fogx.

Q: Suppose that f has an inverse, ƒ(2) = 5, and f'(2) = What is (f~')'(5)? %3D

A: (a) Given that f has an inverse, f(2)=5, and f'(2)=-34 As  f(2)=5 so, f-1(5)=2

Q: (2, 1) Graph of f The derivative of a function fis defined by f'(x) =/1-2 in (2-), -5≤x≤2 where the…

A: Since you posted multiple question, we will solve first question for you. Kindly repost other…

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Q: 6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the…

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Q: Question 19 Suppose that f is continuous on [1,5] and f(x) ≤ 0 if and only if 2 ≤ x ≤ 3. If 3…

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Q: 4. If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? [f{x)–…

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Q: Problem 2 Let f be continuous function on [a, b). (i) Suppose that | f(x)g(x)dx = 0

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Q: 11. Let f(x) = x³ - 2x² + x-1 so f(1) = -1 and f(2)= 1. Let g be the X inverse of f; that is, g(x) =…

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Q: 13. If f is a continuously differentiable real-valued function defined on the open interval (-1, 4)…

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Q: *15. (a) Let f be a function such at |f(x)l s x2 for all x. Prove that f is IS differentiable at 0.…

A: a) Let f(x) be a function with

Q: (5) The following talbe gives values for f,g,f', and gʻ: xf (x)| f' (x) g(x) g'(x) 4 3 2 1 -2 4 4 2…

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Q: Problem 2: Determine whether the function f (x) = 3 - Vx+9 is continuous on the interval [0, 1.

A: Given that:   *The function f(x) is, Since the given function is in fractional form and the…