Final answer:
To evaluate the limit lim x→−∞x²e²ˣ, we can use the L'Hôpital's rule. Taking the derivative of the numerator and the denominator, we find that the limit approaches 0 as x approaches negative infinity.
Step-by-step explanation:
To evaluate the limit lim x→−∞ x²e²ˣ, we can use the L'Hôpital's rule. Taking the derivative of the numerator and the derivative of the denominator, we get:
lim x→-∞ (2xe²ˣ)/(2e²ˣ) = lim x→-∞ x/e²ˣ
As x approaches negative infinity, the exponential term e²ˣ becomes very large compared to x. Therefore, the limit approaches 0, since the denominator grows much faster than the numerator.