Stats Solutions

[Solution Library] Are the following functions R^3→ R continuous at (x,y,z)=(0,0,0) ? f_1(x,y,z)= (x)/(√x^2+y^2+z^2) (x,y,z)≠ (0,0,0) , 0

Question: Are the following functions \({{\mathbb{R}}^{3}}\to \mathbb{R}\) continuous at \(\left( x,y,z \right)=\left( 0,0,0 \right)\) ?

  1. \[{{f}_{1}}\left( x,y,z \right)=\left\{ \begin{aligned} & \frac{x}{\sqrt{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}\,\,\,\,\,\,}\,\,\,\,\left( x,y,z \right)\ne \left( 0,0,0 \right) \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( x,y,z \right)=\left( 0,0,0 \right) \\ \end{aligned} \right.\]
\[{{f}_{2}}\left( x,y,z \right)=\left\{ \begin{aligned} & \frac{xyz}{\sqrt{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}\,\,\,\,\,\,}\,\,\,\,\left( x,y,z \right)\ne \left( 0,0,0 \right) \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( x,y,z \right)=\left( 0,0,0 \right) \\ \end{aligned} \right.\]

Price: $2.99
Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document


∴ Other downloads you may be interested in ∴

log in to your account

Forgot password?
Don't have a membership account?
REGISTER

reset password

Back to
log in

sign up

Back to
log in