Answer
a)2
b) -3 sin x sin y sin z
c) 0
d) 2$\hat x$ + 6x$\hat y$
Work Step by Step
A)
$\frac{∂^2 T_{}a}{∂x^2}$ =2
$\frac{∂^2 T_{}a}{∂y^2}$=0
$\frac{∂^2 T_{}a}{∂z^2}$=0
$\frac{∂^2 T_{}a}{∂x^2}$ + $\frac{∂^2 T_{}a}{∂y^2}$ +$\frac{∂^2 T_{}a}{∂z^2}$ =2
B)
$\frac{∂^2 T_{}b}{∂x^2}$ = $\frac{∂^2 T_{}b}{∂y^2}$=$\frac{∂^2 T_{}b}{∂z^2}$ = - sin x sin y sin z
$\frac{∂^2 T_{}b}{∂x^2}$ + $\frac{∂^2 T_{}b}{∂y^2}$ +$\frac{∂^2 T_{}b}{∂z^2}$ = -3 sin x sin y sin z
C) $\frac{∂^2 T_{}c}{∂x^2}$ = $\frac{∂^2 T_{}c}{∂y^2}$ +$\frac{∂^2 T_{}c}{∂z^2}$ = 0
D) $\frac{∂^2 V}{∂x^2}$ + $\frac{∂^2 V}{∂y^2}$ +$\frac{∂^2 V}{∂z^2}$ = 2$\hat x$ + 6x$\hat y$
