1. Give an example of a bounded function which is not Riemann integrable over (0,1).

Q: Give an example if f : (0,1) -> R that is bounded, continuous but not uniformly continuous on (0,1).

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Q: Let L be the line in R2 through the points [:] } Find a linear functional f and a real number d such…

A: First, we will find the equation of a line given two points.

Q: Prove that if ƒ and g are Riemann integrable on [a, b] then fg is also Riemann integrable on [a, b].…

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Q: Let xn -> 0 and (yn) be bounded. Prove xnyn -> 0.

A: A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k,…

Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

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Q: Define f : R2 → R by letting (y² – x)² (y4 + x²) f(x, y) = if (x, y) # (0, 0), and f(0,0) = 1. ||…

A: The given function is f:ℝ2→ℝ defined as: fx,y=y2-x2y4+x2if x,y≠0,01if x,y=0,0 Claim: The given…

Q: f(z) = f(x+iy) = Z

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Q: Prove there does not exist a continuous function which maps the closed interval [0, 1] onto the open…

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Q: (6) Are all continuous functions on ID differentiable on D?

A: we have to identify the given statement is true or not

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

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Q: Assume that f : (0, 1) → R is a differentiable function with the derivative f' increasing on (0,…

A: Given f:0,1→R is a differentiable function and derivative of f is increasing in 0,1 that is f'x>0…

Q: branch of z1/5 that is not continuous and positive on the imaginary axis?

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Q: f is Riemann integrable iff f is bounded and f has finite set of discontinuous points.

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Q: Suppose that f is differentiable on [a, b]. Prove that if f'(a)f'(b)< 0 then there exists a point c…

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Q: 6. Let f be a continuous function on [0, 2] whose second derivative exists on (0, 2). Assume f(0) =…

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Q: Let f(x)=1/x. Show that f is bounded from above on any interval (α,1), where α>0, but the function…

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Q: 3) √³/₂2 5 - dx -2 2x-1

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Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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