Question
Question 15 (1 point) Find the limit lim _(xarrow 0)(cosmx-cosnx)/(x^2) (n^2-m^2)/(2) (m^2-n^2)/(4) (n^2-m^2)/(4) n^2-m^2 m^2-n^2
Solution
4.7
(240 Votes)
Yale
Elite · Tutor for 8 years
Answer
###
Explanation
## Step 1: Applying L'Hôpital's Rule### Since the limit is in the indeterminate form
as
, we can apply L'Hôpital's Rule. This means we differentiate the numerator and the denominator separately with respect to
.
## Step 2: Applying L'Hôpital's Rule Again### The limit is still in the indeterminate form
, so we apply L'Hôpital's Rule again.
## Step 3: Evaluating the Limit### Now, we can substitute
into the expression.