Question:
If f: R2→R2 is a function defined as \(f(x,y) = \begin{cases} \frac{x}{\sqrt{x^2+y^2}}, & x\neq0,y\neq0\\ 2, & x=0,y=0 \end{cases}\)then, which of the following is correct?
If f: R2→R2 is a function defined as \(f(x,y) = \begin{cases} \frac{x}{\sqrt{x^2+y^2}}, & x\neq0,y\neq0\\ 2, & x=0,y=0 \end{cases}\)then, which of the following is correct?
Updated On: Mar 12, 2025
- f(x,y) is continuous at origin
- f(x,y) is differentiable at origin
- \(\lim\limits_{(x,y)\rightarrow(0,0)}\) f(x,y) exists and is equal to 2
- f(x,y) is not continuous at origin
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct answer is(D): f(x,y) is not continuous at origin
Was this answer helpful?
0
0
Top Questions on Continuity and differentiability
- If \[ f(x) = \begin{cases} \frac{\log(1 + ax) + \log(1 - bx)}{x}, & \text{for } x \neq 0 \\ k, & \text{for } x = 0 \end{cases} \] is continuous at $x = 0$, then the value of $k$ is:
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- (a) Differentiate $\sqrt{e^{\sqrt{2x}}}$ with respect to $e^{\sqrt{2x}}$ for $x>0$.
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- Let \( y=\sin(\cos(x^2)) \). Find \( \frac{dy}{dx} \) at \( x=\frac{\sqrt{\pi}}{2} \).
- CUET (UG) - 2025
- Mathematics
- Continuity and differentiability
- If the function f(x) = $\begin{cases}\frac{k\cos x}{\pi - 2x} & ; x \neq \frac{\pi}{2} \\ 3 & ; x = \frac{\pi}{2} \end{cases}$ is continuous at x = $\frac{\pi}{2}$, then k is equal to
- CUET (UG) - 2025
- Mathematics
- Continuity and differentiability
View More Questions
Questions Asked in CUET PG exam
- Two satellites A and B go around a planet in circular orbits having radii of 4R and R, respectively. If the velocity of satellite A is 3v, the velocity of satellite B will be:
- CUET (PG) - 2025
- Gravitation
- The period of a satellite in a circular orbit of radius 12000 km around a planet is 3 hours. Obtain the period of a satellite in a circular orbit of radius 48000 km around the same planet.
- CUET (PG) - 2025
- Gravitation
- Two satellites A and B of mass 'M' are orbiting the earth in circular orbits at altitudes 2R and 5R respectively, where R is the radius of the earth. The ratio of kinetic energies of satellite A and B will be
- CUET (PG) - 2025
- Gravitation
- Displacement of a particle at any instant of time t is y = 5 sin(100\(\pi\)t + \(\phi\)). The frequency of oscillation of the particle is:
- A tuning fork of unknown frequency sounded with a tuning fork of frequency 256 Hz produces 4 beats per second. If a small quantity of wax is fixed on first fork so that it produces 3 beats per second with tuning fork, what will be the frequency of first fork (in Hz)?
View More Questions