p(x), χ < α q(x), a ≤x≤ b, where q(x) is r(x), x> b on [a, b], which of the following is/are In f(x) continuous always true?

Q: Suppose f : A → B is a function, X ⊂ A and Y ⊂ B. What does it mean to say: (a) z is in the range of…

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A: We have to choose the correct option from the given options according to the given information

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

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Q: the function f is not differentiable at x=0.

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Q: ,10 If f is a continuous function and F'(x)=f(x) for all x € R, then A 2[F(5) – F(1)] B 2[F(10) –…

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Q: Determine all functions f : R → R that have the property that x + y f (x) – f(y) "() - 1e) 2 x – Y…

A: Since x and y are arbitrary points  and f'exists. hence F is continuous and also differentiable. let…

Q: If f is continuous on the interval (-0,00) and f"(x)=3¯*(x- 14) (x– 5)100 , then f(x) has inflection…

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Q: Show that f (x) = is not uni form continuous on (0,3) -3

A: To prove that 1x-3 is not uniformly continuous on 0,3

Q: → R be a function defined by 3x² + x+5 f(x) = not continuous at x = = 0.

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Q: A) If g'(x)>0 for all x in the interval (4,7) then g(x) is for all x on the interval (4,7).| B) If…

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Q: Find continuous functions f1, f2, f3, f4 defined on the open unit interval I = (0, 1) (i.e.…

A: 1. f1(x) = (M1 - L1)x + L1, for all x in (0, 1)  This function is linear and maps (0, 1) onto (L1,…

Q: Let f be a function that is continuous on [1,7] and differentiable on (1,7). Suppose 2 < f'(x) < 3…

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Q: Let /(x)= and g(x) = 2x. For all x-values, g(x) > f(x). f(x)=()* O True O False

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Q: The sketch that represents a continuous function, y = f(x), such that: f'(-3)=Ø f(-3) = 5 and A(1) =…

A: The graph of continuous function f(x) is given in the options. The given data of the function f(x)…

Q: (-2,2), (0,1) (3.0), -5 -3 -2 3. 4. (-2,-1)/ (3.-1) -1 -2- Which statement is true ? A f(x) is not…

A: We know, a continuous function is a real valued function whose graph does not have any breaks or…

Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

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Q: Suppose we have a function f on an interval [a,b] where f(a)=f(b)=0 and f''(x) <= 0 for all x on the…

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Q: 5. Assume f: [0, 1] → [0, 1] is continuous with f(0) = f(1). Prove there are x, y = [0, 1] with |x -…

A: We have to assume f: [0, 1] → [0, 1] is continuous with f(0) = f(1). and prove that there are x, y ∈…

Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: 10. If f(x) is continuous on [a,b], then there exists a c such that: f'(c) = ( f(b) - f(a) ) / (b -…

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Q: Suppose that a < b <c and f is continuous. Select all true statements. (a) f(x) dx = f(x) dx – f(x)…

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Q: Let f and h be real-valued functions continuous on [a, b], differentiable on (a, b), and h(a) not…

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Q: If f is a continuous function on [a, b], and if f (a) = -2 and ƒ (b) = 2, then there exists a real…

A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

Q: 3. Define f(x) so that S(2) = {ap(). f(x) = 0, |피 1 (a) Explain why the function f(x) must be…

A: As per our guidelines we can answer only 3 subparts. please ask others seperately.

Q: (a) g(a) and f(b) = g(b` %3D

A: Define h(x) as h(x)=f(x)-g(x). As both f(x) and g(x) are differentiable, we get h(x) is also…