Question

The vector field F(x,y,z)=⟨2ze^(xy),xy^2z,sin(x+y)cos(z)⟩

is continuous on
Select one:
a. only the point (0,0)
.
b. all of R^2
.

c. all of R^3
.
d. all of R
.

Answer 1

Given $F(x,y,z)=<2ze^{xy},xy^2z,sin(x+y)cos(z)>$ .

Since Polynomial $, e^x, sin(x), cos(x)$ are continuous everywhere, so their composition is also continuous.

Thus, each component of F(x,y,z) are continuous for all $(x,y,z)\in (\R,\R,\R)=\R^3$ .

Hence, option (c) is the correct option.