Question If f(x,y) = fracyx, show that lim(x,y)to(0,0) fracf(x,y)x doe | Mathematics I 2075

Mathematics I207510 marksNumerical: limit, double integralMultiple integrals

Question

If $f(x,y) = \frac{y}{x}$ , show that $\lim_{(x,y)\to(0,0)} \frac{f(x,y)}{x}$ does not exist, justify.

Calculate $\iint_R f(x,y) dA$ , for $f(x,y) = 100 - 6x^2y$ , and $R: 0 \leq x \leq 2, -1 \leq y \leq 1$ . [5+5]

Question

If $f(x,y) = \frac{y}{x}$, show that $\lim_{(x,y)\to(0,0)} \frac{f(x,y)}{x}$ does not exist, justify.

Calculate $\iint_R f(x,y) dA$, for $f(x,y) = 100 - 6x^2y$, and $R: 0 \leq x \leq 2, -1 \leq y \leq 1$. [5+5]

$f(x,y) = \dfrac{y}{x}$ - Required: examine $\displaystyle\lim{(x,y)\to(0,0)} \frac{f(x,y)}{x}$ $\frac{f(x,y)}{x} = \frac{y/x}{x} = \frac{y}{x^2}$ For a limit to exist, it must yield the same finite value along every path to $(0,0)$ . Path 1: $y = 0$ (x-axis) $\lim{x\to 0}\frac{0}{x^2} = 0$ ...

$f(x,y) = \dfrac{y}{x}$ - Required: examine $\displaystyle\lim{(x,y)\to(0,0)} \frac{f(x,y)}{x}$ $$\frac{f(x,y)}{x} = \frac{y/x}{x} = \frac{y}{x^2}$$ For a limit to exist, it must yield the same finite value along every path to $(0,0)$. Path 1: $y = 0$ (x-axis) $$\lim{x\to 0}\frac{0}{x^2} = 0$$ ...

Question If f(x,y) = fracyx, show that lim(x,y)to(0,0) fracf(x,y)x does not exist, justify. Calculate iintR f(x,y) dA, for f(x,y) = 100 - 6x2y, and R: 0 leq x leq 2, -1 leq y leq 1. [5+5]