Limits

Question

Comments

answer will be C

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Can you please explain.

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I found this but it's only written that lim x tends to a g(x) should not be 0 so it may be A or B 

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@Nishtha3121996 I marked 'a' but it was wrong. Answer given is 'C' only.

Answer 1

Option C is the correct answer.

if $_{x \to a}^{lim}$$\frac{f(x)}{g(x)}$ exist then neither $_{x \to a}^{lim}$ f(x) nor $_{x \to a}^{lim}$g(x) may  exist.

eg:-

Let f(x) = $_{x \to 0}^{lim}$$\frac{x}{|x|}$ and g(x) = $_{x \to 0}^{lim}$$\frac{x}{|x|}$

Here for both f(x) and g(x) the limit does not exist since LHL $\neq$ RHL.

But $_{x \to 0}^{lim}$$\frac{f(x)}{g(x)} = 1$