Question

evaluate limit. as lim x approaches - infinity, (x^2)e to the 2x.................. is the answer infinity

Answer 1

No. e^(2x) goes to zero as x --> -infinity
and intuitively, we expect an exponential function to dominate any polynominals, so the overall limit should be zero as well.

Now to prove that, use l'Hopitals rule.

Write x^2.e^(2x) = x^2 / e^(-2x)