Answer
$\triangle z=0.9225$ and $dz=0.9$
Work Step by Step
Write the differential form such as follows:
$dz=(10x) dx+(2y) dy$
$\triangle x=1.05-1=0.05;\\ \triangle y=2.1-2=0.1$
Now, we have
$dz=10 \times (1) (0.05)+2 \times (2) \times (0.1)=0.9$
Thus, we get
$\triangle z=f(1.05,2.1)-f(1, 2)=5x^2+y^2=5(1.05)^2+(2.1)^2-(5+4)$
and $\triangle z \approx 0.9225$
Hence, $\triangle z=0.9225$ and $dz=0.9$