2.66 Let fn(x) = z for all r E R. a) Find the pointwise limit of fn. b) Does f converge uniformly on R? Prove vour conclusion,

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A: To prove thatlimn→∞​yn​−xn​f(yn​)−f(xn​)​=f′(c)given that  f(x)  is differentiable at  c , we follow…

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A: To find: limn→∞-5n2-5n5n2+2n+6

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Q: PROPOSITION Let I be an open interval and suppose f : I → R is differentiable at c e I. If f has a…

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Q: 19) Prove or find a counter example to the following statements: a) f is continuous on (a,b) implies…

A: Step 1: Explanation for question

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Q: ·b 10. (a) Suppose f≥ 0 is continuous on [a, b] and f = 0. Prove that f = 0. a R is continuous and…

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Q: Do part C only Don't use PMI only use given things.

A: Step 1: Define the Slope: Define  m=limx→0​xf(x)​​. This gives the slope of the function near zero,…

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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: X,xif limF,(t)= F(t) at all t for which Fis Continuous

A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: We have fn(x)=nxn(1-x)      for x∈[0,1]a) f(x)=limn→∞fn(x)=limn→∞nxn(1-x) =0     for x∈[0,1]b)  we…

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A: Letxn=1n;  yn=12n 1n-12n=2-12n=12n→0 as n→∞

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Q: Calculus_College 20 (2) Is the function 1:[0,1)+R: (x) - at x-0.1 9x+2 continuoue and differentiable…

A: To find- Is the function f : 0, 1 → ℝ, fx = -2x + 3509x + 2, x = 0.1