Recent questions tagged partial-derivatives / GATE Overflow for GATE CSE

1 votes

0 answers

1

ISI2015-MMA-68
Let $f(x,y) = \begin{cases} e^{-1/(x^2+y^2)} & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0). \end{cases}$Then $f(x,y)$ is not continuous at $(0,0)$ continuous at $(0,0)$ but does not have first order partial derivatives continuous at $(0,0)$ and has first order partial derivatives, but not differentiable at $(0,0)$ differentiable at $(0,0)$

Let $$f(x,y) = \begin{cases} e^{-1/(x^2+y^2)} & \text{ if } (x,y) \neq (0,0) \\ 0 & \text{ if } (x,y) = (0,0). \end{cases}$$Then $f(x,y)$ isnot continuous at $(0,0)$conti...

Arjun

296 views

Arjun asked Sep 23, 2019

0 votes

2 answers

2

ISI2015-MMA-70
Let $w=\log(u^2 +v^2)$ where $u=e^{(x^2+y)}$ and $v=e^{(x+y^2)}$. Then $\frac{\partial w }{\partial x} \mid _{x=0, y=0}$ is $0$ $1$ $2$ $4$

Let $w=\log(u^2 +v^2)$ where $u=e^{(x^2+y)}$ and $v=e^{(x+y^2)}$. Then $\frac{\partial w }{\partial x} \mid _{x=0, y=0}$ is$0$$1$$2$$4$

Arjun

527 views

Arjun asked Sep 23, 2019

1 votes

1 answer

3

ISI2015-MMA-71
Let $f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$ Then $f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ exists $f$ is not continuous at $(0,0)$ ... $f$ is not continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)$ does not exist

Let $$f(x,y) = \begin{cases} 1, & \text{ if } xy=0, \\ xy, & \text{ if } xy \neq 0. \end{cases}$$ Then$f$ is continuous at $(0,0)$ and $\frac{\partial f}{\partial x}(0,0)...

Arjun

408 views

Arjun asked Sep 23, 2019

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