Limits
Limit of GIF
MMTS_Full_Test_20
Grade 12
Question:
$\lim_{x\to\infty}\dfrac{3}{x}\left[\dfrac{x}{4}\right]=\dfrac{p}{q}$ (where $[\cdot]$ denotes GIF), then $p+q$ (where $p,q$ are relative prime) is
Step-by-Step Solution
Key Concept: $\left[\frac{x}{4}\right]\approx\frac{x}{4}$ as $x\to\infty$
$\lim_{x\to\infty}\frac{3}{x}\cdot\frac{x}{4}=\frac{3}{4}$. So $p=3,q=4$, $p+q=7$.
Correct Answer: 2