Evaluate the limit using L'Hopital's Rule if necessary.
A) 0
D) 1
E) does not exist

Question

Evaluate the limit  using L'Hopital's Rule if necessary.
A) 0 
D) 1 
E) does not exist

Quizplus · Accepted Answer

The given expression can be simplified as:

lim a → ∞ 11*e^(a^2)/(a^2+1)

Since the numerator and denominator both approaches infinity as a approaches infinity, we can use L'Hopital's Rule here.

Differentiating numerator and denominator with respect to a, we get:

lim a → ∞ (2*a*11*e^(a^2))/(2*a)

= lim a → ∞ 11*e^(a^2)

Since e^(a^2) grows faster than a^2, the denominator (a^2+1) can be ignored as a becomes very large. Hence, the limit is:

lim a → ∞ 11*e^(a^2) = ∞

Therefore, the limit does not exist, and the correct answer is (E).

Evaluate the Limit Using L'Hopital's Rule If Necessary