How do you find #\lim _ { x \rightarrow - \frac { x } { 4} } \frac { \cos 2x } { \sin x + \cos x }#?
2 Answers
Explanation:
First investigate: Substitute
Since:
We end up with the indeterminate form
This rule states:
If,
Then,
So,
Substitute in
Simplify by applying the exponent rule:
Use
Explanation:
# = lim_(xrarr-pi/4)((cosx-sinx)(cosx+sinx))/(cosx+sinx) #
# = lim_(xrarr-pi/4)(cosx-sinx))#
# = cos(-pi/4) - sin(-pi/4)#
# = sqrt2/2-(-sqrt2/2) = sqrt2#