Prove that if f: [0, 1] → R is a continuous function, then Find Prove that 1 n n k=1 f lim n1x ())-[² → n 1² we + 2² √e² n³ lim n² n→∞ f(x) dx, as na n + n² wen k k4 + nª || FI∞o

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Q: z +3 - iv2 lim z--3+iv2 z² + 6z + 11 1. 2.

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Q: if f:[0,2] 3 R such that if x>0 f(x) = { ²2 if x<0 show that whether f is continuous in [0,2]

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Q: lim 3i 4 +

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A: Let f: ℝ→ℝ be a differentiable function. (a) Suppose f'x≥1 for all x∈ℝ. Let K⊂ range (f) be a…

Q: 5) Consider the function. f(x) = x≤2 (3-2x, 1₂. 3x x>2 a) Find the left-hand and right-hand limits…

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Q: Let Show f is defined for all x &gt; 0. Is f continuous on (0,∞)? How aboutdifferentiable?

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Q: 3. Let f: R-R be defined by f(x) = (2x + 1)2. Use the definition of continuity to show that fis…

A: I have explained everything with in the solution. Please go through that.

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Q: Let fn f, where if 0<<! Sn(x) ={ S 2-a if 0<x<1 and f(x) if a = 0 Then lim sup fn (x) – ƒ (x)| =

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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.

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Q: Define limit of a function g(x) at x = a. 3+2x for -sx<0 for 0sx< |-3-2x for x 2 Given, f(x) = 3-2x…

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