Question

求极限 lim (1+3tanx平方)的1/x的平方 x趋于0

Answer 1

设y=(1+3tanx²)^(1/x)

lny=ln(1+3tanx²)/x

lim0> ln(1+3tanx²)/x

=lim 6x/((cos²x²)*(1+3tanx²))

=lim 6x/(cos²x²+3sinx²*cosx²)=0/1=0

所以

lim (x->0) (1+3tanx²)^(1/x)=lim (x->0) y

=lim (x->0)e^(lny)=e^0=1