Question

limit help

Answer 1

\(lim_{t\rightarrow 0^+} \dfrac{4+2i\pi}{t^3}e^{-(2+i\pi)/t^2} = ?\)

Answer 2

Let \(x=\dfrac{1}{t}\) so that as \(t\to0^+\) you have \(x\to\infty\), and
\[\lim_{t\to0^+}\frac{4+2i\pi}{t^3}e^{-(2+i\pi)/t^2}=2\lim_{x\to\infty}\frac{kx^3}{e^{kx^2}}\]
where \(k=2+i\pi\).

Answer 3

Then use L'hopital rule to get 0?

Answer 4

Sure, or possibly the squeeze theorem. Your choice.

Answer 5

Thank you. I confused when I see t^3 at the denominator. If t goes to 0 , it should be infinitive, not 0 as required.

Answer 6

I find that substitutions can often be quite helpful in making confusing limits more approachable :)