Question:medium

If \( f(x) = \begin{cases} \frac{\sin |x|}{x}, & \text{for } [x] \ne 0 \\ 0, & \text{for } [x] = 0 \end{cases} \) where, \([x]\) denotes the greatest integer less than or equal to \(x\), then \(\lim_{x \to 0} f(x)\) is equal to

Show Hint

For greatest integer function, always check left-hand and right-hand limits separately.

Updated On: Apr 16, 2026

1
-1
0
Does not exist

Show Solution

The Correct Option is D

Solution and Explanation

Was this answer helpful?

Questions Asked in MET exam

Let \( D = \begin{vmatrix} n & n^2 & n^3 \\ n^2 & n^3 & n^5 \\ 1 & 2 & 3 \end{vmatrix} \). Then \( \lim_{n \to \infty} \frac{M_{11} + C_{33}}{(M_{13})^2} \) is:

MET - 2024
Determinants

View Solution

Given vectors \(\vec{a}, \vec{b}, \vec{c}\) are non-collinear and \((\vec{a}+\vec{b})\) is collinear with \((\vec{b}+\vec{c})\) which is collinear with \(\vec{a}\), and \(|\vec{a}|=|\vec{b}|=|\vec{c}|=\sqrt{2}\), find \(|\vec{a}+\vec{b}+\vec{c}|\).

MET - 2024
Addition of Vectors

View Solution

Given \(\frac{dy}{dx} + 2y\tan x = \sin x\), \(y=0\) at \(x=\frac{\pi}{3}\). If maximum value of \(y\) is \(1/k\), find \(k\).

MET - 2024
Differential equations

View Solution

A real differentiable function \(f\) satisfies \(f(x)+f(y)+2xy=f(x+y)\). Given \(f''(0)=0\), then \[ \int_0^{\pi/2} f(\sin x)\,dx = \]

MET - 2024
Definite Integral

View Solution

If \( f(x) = \begin{cases} \frac{\sin |x|}{x}, & \text{for } [x] \ne 0 \\ 0, & \text{for } [x] = 0 \end{cases} \) where, \([x]\) denotes the greatest integer less than or equal to \(x\), then \(\lim_{x \to 0} f(x)\) is equal to

Show Hint

The Correct Option is D

Solution and Explanation

Top Questions on limits and derivatives

Questions Asked in MET exam