Evaluate the limit

Question

Can i get help Thanks.I’m stuck on this

limit

x approaches negative infinity (1.01^x+x^1000)/(e^x+x^3)

Answer 1

Lim 1.01^x+x^(1000/(e^x+x^3) =Lim 1.01^x+Lim x^1000/(e^x+x^3)=0+lim x^1000/(e^x+x^3). Let y=x^1000/(e^x+x^3). Find ln(y)=1000/(e^x+x^3)ln(x) = 1000lim(1/x/(e^x+3x^2))=0. Since Lim ln(y)=0 then lim y=1. The answer = 1