Question

请问，这道高数题怎么写啊

请问，这道高数题怎么写啊写不来了

Answer 1

先解出定积分
u=sinnx ncosnx -n²sinnx

v'=e^x e^x e^x
∫(0,1)e^xsinnxdx
=(e^xsinnx-e^x·ncosnx)(0,1)-n²∫(0,1)e^xsinnxdx
∫(0,1)e^xsinnxdx=1/(n²+1)(e^xsinnx-e^x·ncosnx)(0,1)
=1/(n²+1)(esinn-necosn+n)
所以
原式=lim(n->∞)(esinn-necosn+n)/(n²+1)
=0