a) \(\lim \frac{n}{n^{2}2014}=\lim \frac{1}{\frac{n^{2}2014}{n}}=\lim \frac{1}{n2014}=\frac{1}{+\infty }=0\)
b) Cálculo auxiliar:
Anexo:
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\(\frac{n+1}{n+2}=1+\frac{-1}{n+2}\)
\(\lim \frac{\left ( n+1 \right )^{\frac{1}{2}}}{\left ( n+2 \right )^{\frac{1}{2}}}=\lim \left ( \frac{n+1}{n+2} \right )^{\frac{1}{2}}=\lim \left ( 1+\frac{-1}{n+2} \right )^{\frac{1}{2}}=\left (1+\frac{-1}{+\infty } \right )^{\frac{1}{2}}=\left ( 1+0 \right )^{\frac{1}{2}}=1\)
ou a partir do 2º passo \(\left [ \lim \left ( \frac{n+1}{n+2} \right ) \right ]^{\frac{1}{2}}=\left [ \lim \left ( \frac{n}{n} \right ) \right ]^{\frac{1}{2}}=1^{\frac{1}{2}}=1\)
Caso tenha dúvidas não hesite em dizer.