Question #5f7a4
1 Answer
This limit can be found using l'Hopital's rule or by using knowledge of trigonometry.
Explanation:
If you try rewriting to get a fundamental trigonometric limit, you'll get:
This limit has indeterminate form:
If you have learned it, you can use l'Hopital's rule on the original ratio form.
Without l'Hopital
Use a 'trick' you may recall from trigonometry. (It shows up in some identity problems.)
# = (1-cos^2x)/(x^2(1+cosx))#
# = sin^2x/(x^2(1+cosx))#
Now, we can split this into factors whose limits we can find.
# = sinx/x sinx/x 1/(1+cosx)#
# = (1)(1)(1/(1+1))#
# = 1/2#