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Problem $4(15+15=30$ points $)$ (a) Consider the sequence $(f_{n})$ defined as follows: $f_{n}(x)={x/n1/n?ifnis evenifnis odd?$ First, determine the pointwise limit. Next, show that for every $a>0$ the sequence $(f_{n})$ converges uniformly on the interval $[?a,a]$. Is the convergence uniform on $R$ ? (b) Consider the sequence $(g_{n})$ defined as follows: $g_{n}(x)=cos(x/n).$ First, determine the pointwise limit. Next, show that for every $a>0$ the sequence $(g_{n})$ converges uniformly on the interval $[?a,a]$. Is the convergence uniform on $R$ ?

(a) Here let fn(x) converges to f(x)Hence, lim?fn(x)=limn??xn=0and lim?fn(x)=limn??1n=0Hence, the poin

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