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

$\text{Since, we have}\\ F(x,y,z)=⟨2ze^{xy},xy^2z,sin(x+y)cos(z)⟩\\ \text{So, we get}\\ F(x,y,z) \text{ is continuous in } R^3.\\ \text{This implies that the correct }\\ \text{answer is} \ \ c$