Question

当x趋近于正无穷时 (1+x^ 2)^ 1/x的极限是多少 麻烦写下详细过程

Answer 1

当x趋近于正无穷时 (1+x^ 2)^ 1/x

=e^lim(x->+∞)[ln(1+x²)】/x

=e^lim(x->+∞)2x/(1+x²)/1

=e^0

=1