lim(x^2/exp(-x), x->-inf) — step-by-step solution

Let's evaluate the limit of

\frac{x^{2}}{\exp (- x)}

when

x \to -∞

ⓘ A quantity that grows without bound raised to a positive power still grows without bound, to a negative power it tends to 0

The limit of

x^{2}

+∞

when

x \to -∞

ⓘ We use a reference limit of the function exp

The limit of

\exp (- x)

+∞

when

x \to -∞

For

\frac{x^{2}}{\exp (- x)}

, we encounter the indeterminate form

\frac{+∞}{+∞}

x

tends to

-∞

Comparative growth shows that

\exp (- x)

dominates

x^{2}

x \to -∞

So the limit of

\frac{x^{2}}{\exp (- x)}

0

⁺ when

x \to -∞

▶Limit:

0