Question

19. Evaluate the limit $$ \lim_{(x,y) \to (0,0)} \frac{xy}{x^2+y^2} $$ as $(x,y)$ approaches the origin along: (a) The $x$-axis. (b) The $y$-axis. (c) The line $y=mx$. (d) The spiral $r=\theta$, $\theta>0$. (e) The differentiable curve $y=f(x)$, with $f(0)=0$. (f) The arc $r=\sin 3\theta$, $\frac{1}{6}\pi < \theta < \frac{1}{3}\pi$. (g) The path $r(t) = \frac{1}{t} \mathbf{i} + \frac{\sin t}{t} \mathbf{j}$, $t>0$.

Name: 19 evaluate the limit limxy to 00 fracxyx2y2 as xy approaches the origin along a the x axis b the y axis c the line ymx d the spiral rtheta theta0 e the differentiable curve yfx with f00 f 81258
Uploaded: 2021-08-26T06:47:50-08:00
Duration: 4 min 7 s
Channel: Harshita Goel
Description: 19 evaluate the limit limxy to 00 fracxyx2y2 as xy approaches the origin along a the x axis b the y axis c the line ymx d the spiral rtheta theta0 e the differentiable curve yfx with f00 f 81258

          19. Evaluate the limit
$$ \lim_{(x,y) \to (0,0)} \frac{xy}{x^2+y^2} $$
as $(x,y)$ approaches the origin along:
(a) The $x$-axis.
(b) The $y$-axis.
(c) The line $y=mx$.
(d) The spiral $r=\theta$, $\theta>0$.
(e) The differentiable curve $y=f(x)$, with $f(0)=0$.
(f) The arc $r=\sin 3\theta$, $\frac{1}{6}\pi < \theta < \frac{1}{3}\pi$.
(g) The path $r(t) = \frac{1}{t} \mathbf{i} + \frac{\sin t}{t} \mathbf{j}$, $t>0$.

$19 evaluate the limit limxy to 00 fracxyx2y2 as xy approaches the origin along a the x axis b the y axis c the line ymx d the spiral rtheta theta0 e the differentiable curve yfx with f00 f 81258$

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