This's a question in chapter 2.1, #56:
( sin(x)-x )/x^3
calculate the limit as x approaching 0.
since as x approaches 0, it's will be 0/0, in this case, am i allowed to use L'H˘pital's Rule twice so that i can degrade the power of denominator? Besides, sin(x)/x is equal to 1,so that the limit will be -1/6 ?
Appreciate for your time.
No: you may not apply L'Hopital to problems (in quizzes and exams); we have not covered it, and we will not cover it in this course. Each problem should be interpreted as stating "solve or prove using the theory covered so far".
[I would have appreciated if you had stated the question as in the textbook (the statement in the text starts with "it is impossible to compute the limit [above] algebraically" etc.) . I do not drag the text with me, and the question that you have typed above is misleading since it is very hard to deduce it from the theory we have developed so far (I needed some time to realize that).]