Thank you for helping! While uniform convergence can preserve continuity, it doe

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While uniform convergence can preserve continuity, it does not preserve differentiability. Find an explicit example of a sequence of differentiable functions on [-1, 1] that converge uniformly to a function f such that f is not differentiable. Hint: Consider |x|1+1/n, show that these functions are differentiable, converge uniformly, and then show that the limit is not differentiable.

Explanation / Answer

as per question consider y=|x|^1+1/n dy/dx=(1+1/n)|x|^1/n at x=0 dy/dx=0 at both sides of 0 so differentiable and at n-->infinity x-->infinity now for limit at x=0+ y=some positive value at x=0- y=some negative value so,limit doesnot exist

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