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

Q: Show that the function f defined by (r, y) = (0,0) f(x, y) = { 22 + y (r, y) # (0,0) x + y

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

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

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

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Q: Show that the function f (z) = Z is continuous at the point z=0 but not differentiable at z=0.

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Q: Is the function f : Z→Z defined as f(n)=n^3+2 one-to-one ?

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Q: Let f be analytic in a region G. If f(g) lies on the parabola u=v^2, prove that f is constant in G.

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Q: Let f(x, y) = x* /I Evaluate f(3, 0)

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Q: Determine the value of m such that the function *- y - 2 E + 2 vỹ VI – Vy ; z +y f(x, y) = is…

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Q: Show that A Function with a Single Point of Discontinuity 2xy x² +1,²² 0, is continuous at every…

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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: Q2) homeomorphism. Prove or disprove: The function f: (R, T1) - (R, 13) defined by f(x) = 3x is a…

A: Clearly the given function f(x)=3x is continuous. Now we want to check whether it is bijective,

Q: A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is…

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Q: Use a truth table to determine whether the argument below is valid or invalid. pA (q V r) ... ~pV ~…

A: Given argument p∧q∨r~q∨~r

Q: What would be an example of a function that is not integrable on [2, 10] and why is it not…

A: Consider a function: y=1x-2……1

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: Assume that f(x, y) is a function given by if (r, y) # (0,0), f(x, y) 0 if (r, y) = (0, 0). Page 1…

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Q: If f (s Continuous then on -fex) True or felse?

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Q: Let f(x, y) = (- (3z + y))°. Then

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Q: Show that f = {(x, y) ∈ R × R; x = y^3} is a function from R to R

A: Given, The function f={(x,y)∈R×R ; x=y3 }   We have to show that the given function is from R to R.

Q: Let f : R2 → R with f(x,y) = px^2 + y^2. Sketch the graph of f. Prove that f is not differentiable at…

A: Given f(x,y)=px2+y2

Q: Prove that f (z) =zz is nowhere analytic

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Q: Without using the Cauchy-Riemann equations, investigate the differentiability of the function f(z) =…

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Q: What is an example of a function f : [2, 3] -->R which is not continuous at 1 but which is…

A: Here's an example of a function that is not continuous at 1 but is integrable on the interval [2,…

Q: Let f.9: E1-00, +00] be two integrable functions. Using the fact for non-negative functions, prove…

A: Given that f,g:E→−∞,∞ be two integrable  and no-negative function. We have to prove that…