lim(x→0)(e^x^2-cosx)/(3^x-1)sinx
=lim(x→0)[(e^x^2-1)+(1-cosx)]/(3^x-1)sinx
=lim(x→0)[x^2+x^2/2]/xln3sinx
=lim(x→0)[3x^2/2]/x^2ln3
=3/(2ln3)