If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the following is FALSE? b Ⓒkdx A kdx=bk-ak a b ℗ [ f(x) g(x) dx = [ f* f(x) dx][√ * g(x)ªx] B dx a a a b b (C) Skl Skf(x) dx = k f(x) dx a b b b ℗ √ [f(x) = g(x)]dx = f(x) f(x) dx - g(x) dx a a

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Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

Q: if f(x) is continuous on [a, b], then we can always say that: Select one: O True O False a b a…

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Q: For what value of k is f(x) continuous at x=3? f(x) = (x-1)(x-3) 9-x² 3k, x=3 " x!= 3 (when x is not…

A: f(x)={(x−1)(x−3)9−x2,x!=3( when x is not equal to 3)3k,x=3

Q: 4

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Q: a) f(x)dx = 0 -- b) f?(x)dx = 2 | f²(x)dx -h

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Q: n a and b with f(c) = N. I thi

A: Mean value theorem: Rolles theorem If a real-valued function f is continuous on a proper  [a, b],…

Q: Show that if f"(x) < 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] < favg < f[(a+b)/2]

A: Consider the given information. f"(x) &lt; 0 for x ∈ [a, b], then 1/2[f(a) + f(b)] &lt; favg &lt;…

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Q: 2. Let f(x) = 1 for rational x and f(x) = 0 for irrational x. Show that if F is increasing and…

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Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5