Question

Find the indicated limit.

lim (4sinx−5x6x)
x→0

Answer 1

To find the limit of the given expression, we can use L'Hopital's Rule. By differentiating the numerator and denominator and substituting x = 0, we find that the limit is -1/6.

Step-by-step explanation:

Let's evaluate the limit:

lim (4sinx-5x/6x) as x approaches 0.

First, let's substitute x = 0 into the expression:

(4sin(0)-5(0))/(6(0)) = 0/0, which is an indeterminate form.

To evaluate this limit, we can use L'Hopital's Rule.

Applying L'Hopital's Rule, we differentiate the numerator and denominator with respect to x:

lim (4cosx - 5)/(6) as x approaches 0.

Now, substituting x = 0 into the expression:

(4cos(0) - 5)/(6) = (4 - 5)/(6) = -1/6.

Therefore, the limit is -1/6.