Is 100−1 an indeterminate form? I thought only 00,∞∞ and any form that can be represented in those two are indeterminate. Moreover, how do we know if a form is indeterminate?
P.S.
For people who says that this question doesn't reflect OP's effort, I came through it when calculating limt→012sin2t2sint(1−cost)(t−sint)−1.
Answer
Let us consider the main purpose of this topic to solve the limit and discuss the method of solving it.
As I mentioned in the comments, the use of L'Hopital's rule is not determined by some or other "indeterminate forms". The theorem has very specific assumptions. Furthermore, I do not know what it means to be "completely indeterminate" and how that would specify the condition of being "indeterminate".
Suppose we needed to find limt→0f(t)g(t)
If limt→0f(t)=limt→0g(t)=0 OR limt→0f(t)=±∞ and limt→0g(t)=±∞, then
limt→0f(t)g(t)=limt→0f′(t)g′(t)
Of course, f and g must be differentiable around t=0, but that is not an obstacle for this particular problem.
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