As far as I know, 0∞ is not an indefinite form and it goes to zero. Then the limit of (cosx)tanx when x goes to π/2− should equal 0.
But after log transformation, its limit is ∞. I am not sure which one is correct, zero or infinity?
Thanks for your help.
I slightly changed the question. I realized that x goes to π/2− (left hand limit) in the original question.
Answer
Suppose that f and g are functions such that as x→a, f(x)→0 and g(x)→∞, and consider h(x)=f(x)g(x). We know that
lim
Thus,
\lim_{x \to a} h(x) = 0.
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