Lim x趋近π,sin3x/(x-π),等于多少?lim x趋近∞,[x/(1+x)]^x,等于多少?

Question

Lim x趋近π,sin3x/(x-π),等于多少?lim x趋近∞,[x/(1+x)]^x,等于多少?

Answer 1

sin3x/(x-π)=sin3(t+π)/t【t趋于0】=sin(3t+3π)/t=-sin3t/t=-3
[x/(1+x)]^x=[1-1/(1+x)]^x={[1-1/(1+x)]^-(1+x)}^[-x/(1+x)]=e^(-1)=1/e