MHT CET · Maths · Limits
\(\lim _{x \rightarrow 3} \frac{(84-x)^{\frac{1}{4}}-3}{x-3}\) is
- A \(\frac{-1}{108}\)
- B \(\frac{-1}{84}\)
- C \(\frac{-1}{27}\)
- D \(\frac{-1}{4}\)
Answer & Solution
Correct Answer
(A) \(\frac{-1}{108}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 3} \frac{(84-x)^{\frac{1}{4}}-3}{x-3}\) is of \(\frac{0}{0}\) form. Apply L'Hôpital's Rule: \(\lim _{x \rightarrow 3} \frac{\frac{1}{4}(84-x)^{\frac{1}{4}-1}(-1)}{1}\)
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