SOLUTION: Use L'Hopital's rule to determine lim {tanx-x/sinx-x}, for x tend to 0

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Question 1183258: Use L'Hopital's rule to determine lim {tanx-x/sinx-x}, for x tend to 0
Found 2 solutions by Solver92311, robertb:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


You have to apply L'Hôpital three times. The first two times you will still have the indeterminate form, but the third time, you will get in the limit.

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
lim%28x-%3E0%2C+%28tanx+-+x%29%2F%28sin+x+-+x%29%29
lim%28x-%3E0%2C+%28%28sec+x%29%5E2+-+1%29%2F%28cos+x+-+1%29%29, by direct application of L'Hopital's rule
.

Hence we have only used L'Hopital's rule once and have avoided its unnecessary multiple use by doing only basic trigonometric manipulation.