Question

Evaluate the limit using l'hospital's rule lim 12xe^(1/x) - 12x

Answer 1

To evaluate the limit using L'Hôpital's rule, differentiate the numerator and the denominator separately. Then, evaluate the limit of the derivatives of the numerator and denominator as x approaches the given value.

Step-by-step explanation:

To evaluate the limit using L'Hôpital's rule, we first differentiate the numerator and the denominator separately.

Let's differentiate the numerator:

f'(x) = 12e^(1/x) - 12

Now, let's differentiate the denominator:

g'(x) = 1

We can now evaluate the limit by taking the limit of the derivative of the numerator divided by the derivative of the denominator as x approaches the given value.

lim(x -> a) f'(x) / g'(x)

Where 'a' is the value the limit is approaching. In this case, 'a' is the value given in the question.