Suppose g : (0, 1) ? R is a bounded, continuous function. Define f : [0, 1] ? R by f(x)= 0 if x=0…

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If f:[0,1]→R is a continuous function, then ⁡∫(nf(x))/(1+n^2 x^2 )dx→π/2 f(0) as n→∞. If f:[0,1]→R is a continuous function, then ⁡∫(nf(x))/(1+n^2 x^2 )dx→π/2 f(0) as n→∞.
Suppose that the function `f, g, f Suppose that the function `f, g, f',and g'` are continuous over `[0,1], g(x) !=0` for `x in [
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let a and c are real number,cand f is on [-1,1] byf(x)={x^a sin(x^-1),if x≠0,0 if x=0} f let a and c are real number,cand f is on [-1,1] byf(x)={x^a sin(x^-1),if x≠0,0 if x=0} f' is bounded
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