JEE Mains · Maths · STD 12 - 6. Application of derivatives
Let \(f: \rightarrow R \rightarrow(0, \infty)\) be strictly increasing function such that \(\lim _{x \rightarrow \infty} \frac{f(7 x)}{f(x)}=1\). Then, the value of \(\lim _{x \rightarrow \infty}\left[\frac{f(5 x)}{f(x)}-1\right]\) is equal to
- A \(4\)
- B \(0\)
- C \(7 / 5\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
\( f: R \rightarrow(0, \infty)\) \( \lim _{x \rightarrow \infty} \frac{f(7 x)}{f(x)}=1 \) \( \because \mathrm{f} \text { is increasing } \) \( \therefore \mathrm{f}(\mathrm{x})<\mathrm{f}(5 \mathrm{x})<\mathrm{f}(7 \mathrm{x})\)…
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