Assertion : If a and b are positive and [x] denotes greatest integer _ x 0^ + x a [ ~b x…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Assertion : If a and b are positive and [x] denotes greatest integer < x, then
\(\lim _{\mathrm{x} \rightarrow 0^{+}} \frac{\mathrm{x}}{\mathrm{a}}\left[\frac{\mathrm{~b}}{\mathrm{x}}\right]=\frac{\mathrm{b}}{\mathrm{a}}\)
Reason : \(\lim _{x \rightarrow \infty} \frac{\{x\}}{x}=0\) where {x} denotes fractional part of x.
\(\lim _{\mathrm{x} \rightarrow 0^{+}} \frac{\mathrm{x}}{\mathrm{a}}\left[\frac{\mathrm{~b}}{\mathrm{x}}\right]=\frac{\mathrm{b}}{\mathrm{a}}\)
Reason : \(\lim _{x \rightarrow \infty} \frac{\{x\}}{x}=0\) where {x} denotes fractional part of x.
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(A) If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
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