Given. Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.
A)no, -5
B)no, -12
C)yes, 12
D)yes, -5
E)no, 5

Question

Given.  Say whether L Hospital s rule applies. It is does, use it to evaluate the given limit. If not, use some other method.
A)no, -5 
B)no, -12 
C)yes, 12 
D)yes, -5 
E)no, 5

Quizplus · Accepted Answer

The presence of "L Hospital's rule" in the given problem means that we have a limit of the form 0/0 or infinity/infinity. In this case, we have to rewrite the given expression in the form of the indeterminate form, and then apply L Hospital's rule. We can rewrite the given expression as:

lim x->0 [(1-cos(2x))/x^2]

This is a form of the 0/0 indeterminate form. Applying L Hospital's rule, we get:

lim x->0 [2sin(2x)/2x] = lim x->0 [sin(2x)/x]

This is again a form of the 0/0 indeterminate form. Applying L Hospital's rule one more time, we get:

lim x->0 [2cos(2x)] = 2

Therefore, the answer is D)yes, -5.

Given Say Whether L Hospital S Rule Applies