${ message }
Your cart is empty
Discount (${discount_percentage}%) : - ${discount}KD
Need Help?
How was the speed of the video ?
How well did you understood the video ?
Was the video helpful?
Was the notes helpful?
Sign up to try our free practice
KD
19.500
1 month
Add to cart
42.500
4 months
Subscribe to Calculus C
Practice (Free)
Practice
Q1: Find the limit if it exist?
$$\lim _{(x, y) \rightarrow\left(2, -1\right)} \frac{x^{2} y+x y^{2}}{x^{2}-y^{2}} $$
$$\lim _{(x, y) \rightarrow(2, -1)} \frac{4 \times -1+2 \times 1}{4-1} $$
$$=\frac{-4+2}{3} $$
$$=\frac{-2}{3} $$
Q2: Find the limit if it exist?
$$\lim _{(x, y, z) \rightarrow(0, 0, 0)} \frac{x y+y z}{x^{2}+y^{2}+z^{2}} $$
(1) $$\lim _{(x, y, z) \rightarrow(0,0,0)} \frac{0+0}{0}=\frac{0}{0}$$
(2) check
$$x=y$$ $$x=2$$
$$\lim _{\left(x, y, z\right) \rightarrow (0,0,0)} \frac{x^{2}+x^{2}}{x^{2}+x^{2}+x^{2}} $$
$$=\frac{2 x^{2}}{3 x^{2}}=\frac{2}{3} $$
$$x=0$$ $$y=0$$
$$\lim _{\left(x, y, z\right) \rightarrow (0,0,0)} \frac{0+0}{0+0+z^{2}}=0$$ Limit doesn't exist
Q3: Determine the set of points at which the function is continuous
$$f(x, y)=\frac{x y}{1+e^{x-y}} $$
Req: {points} $$\Rightarrow$$ continuous
(1) $$1+e^{x-y} \neq 0$$
(2) $$1+e^{x-y}>0, \quad e^{x-y}>0 \quad$$ for all $$(x, y)$$
(3) Continass on $$R^{2}$$
Q4: Determine the set of points at which the function is continuous
$$f(x, y, z)=\sqrt{y-x^{2}} \ln Z$$
(1)
1. Limil exist 2. $$f(x, y, z)$$ defined. 3- $$\lim f(x, y, z)=f(x, y, z)$$
(2) $$y-x^{2} \geq 0$$
$$y \geq x^{2} $$
(3) $$\ln z \rightarrow z>0$$
$$f(x, y, z)$$ continuous $$y \geq x^{2}, z>0$$
No comments yet
Q1: Find the limit if it exist?
$$\lim _{(x, y) \rightarrow\left(2, -1\right)} \frac{x^{2} y+x y^{2}}{x^{2}-y^{2}} $$
$$\lim _{(x, y) \rightarrow(2, -1)} \frac{4 \times -1+2 \times 1}{4-1} $$
$$=\frac{-4+2}{3} $$
$$=\frac{-2}{3} $$
Q2: Find the limit if it exist?
$$\lim _{(x, y, z) \rightarrow(0, 0, 0)} \frac{x y+y z}{x^{2}+y^{2}+z^{2}} $$
(1) $$\lim _{(x, y, z) \rightarrow(0,0,0)} \frac{0+0}{0}=\frac{0}{0}$$
(2) check
$$x=y$$
$$x=2$$
$$\lim _{\left(x, y, z\right) \rightarrow (0,0,0)} \frac{x^{2}+x^{2}}{x^{2}+x^{2}+x^{2}} $$
$$=\frac{2 x^{2}}{3 x^{2}}=\frac{2}{3} $$
$$x=0$$
$$y=0$$
$$\lim _{\left(x, y, z\right) \rightarrow (0,0,0)} \frac{0+0}{0+0+z^{2}}=0$$
Limit doesn't exist
Q3: Determine the set of points at which the function is continuous
$$f(x, y)=\frac{x y}{1+e^{x-y}} $$
Req: {points} $$\Rightarrow$$ continuous
(1) $$1+e^{x-y} \neq 0$$
(2) $$1+e^{x-y}>0, \quad e^{x-y}>0 \quad$$ for all $$(x, y)$$
(3) Continass on $$R^{2}$$
Q4: Determine the set of points at which the function is continuous
$$f(x, y, z)=\sqrt{y-x^{2}} \ln Z$$
(1)
1. Limil exist
2. $$f(x, y, z)$$ defined.
3- $$\lim f(x, y, z)=f(x, y, z)$$
(2) $$y-x^{2} \geq 0$$
$$y \geq x^{2} $$
(3) $$\ln z \rightarrow z>0$$
$$f(x, y, z)$$ continuous $$y \geq x^{2}, z>0$$
No comments yet
Join the conversation