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Question: Answered & Verified by Expert
$\lim _{x \rightarrow a} f(x) . g(x)$ exists, if
MathematicsLimitsJEE Main
Options:
  • A $\lim _{x \rightarrow a} f(x)$ and $\lim _{x \rightarrow a} g(x)$ exist
  • B $\lim _{x \rightarrow a} f(x)^{g(x)}$ exists
  • C $\lim _{x \rightarrow a} \frac{f(x)}{g(x)}$ exists
  • D $\lim _{x \rightarrow a} f(x) g\left(\frac{1}{x}\right)$ exists
Solution:
2280 Upvotes Verified Answer
The correct answer is: $\lim _{x \rightarrow a} f(x)$ and $\lim _{x \rightarrow a} g(x)$ exist
If both \(\lim _{x \rightarrow a} f(x)\) and \(\lim _{x \rightarrow a} g(x)\) exist, then \(\lim _{x \rightarrow a} f(x) \cdot g(x)\) also exists by the product limit rule.

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