Consider sequences of functions fn(x)=nx/1+n^2x^2 and gn(x)=dfrac x1+nx^2, xle1.

(B) Sequence fn is not uniformly convergent but sequence gn is uniformly convergent

Q23Section II (Mathematics)23 of 84

$f_n$ keeps a bump of height $\tfrac12$ at $x=1/n$ ; $g_n$ 's bump shrinks like $1/\sqrt n$

Consider sequences of functions $f_n(x)=\dfrac{nx}{1+n^2x^2}$ and $g_n(x)=\dfrac x{1+nx^2}$ , $|x|\le1$ .

Pick an option to check your answer.

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