I'm trying to solve this limit
limx→0sinx−xx3
Solving using L'hopital rule, we have:
limx→0sinx−xx3=limx→0cosx−13x2=limx→0−sinx6x=limx→0−cosx6=−16.
Am I right?
I'm trying to solve this using change of variables, I need help.
Thanks
EDIT
I didn't understand the answer and the commentaries, I'm looking for an answer using change of variables.
Answer
I suppose the below counts as a change of variable.
Assuming that the limit exists, then you can compute the limit as follows:
Replace x by 3x, then the limit (say L) is
L=limx→0sin3x−3x27x3=limx→03sinx−3x−4sin3x27x3=
limx→019(sinx−xx3)−limx→0427(sin3xx3)
(we used the formula sin3x=3sinx−4sin3x).
Thus we get
L=L9−427⟹L=−16
Of course, we still need to prove that the limit exists.
No comments:
Post a Comment