find the total differential of...

Question

z=f(x,y)=sqrt(x^2+y^2) and compute its value when (x,y)= (-3,4) and (dx,dy)=(0.02,0.01)

b. Using the total differentials, approximate sqrt( (12.001)^2+(4.998)^2 )

Answer 1

(b)

The function is  .

Find the approxiamte value of .

The total differential is .

Consider  and .

Find   and .

.

Apply partial derivative on each side with respect to .

.

Apply partial derivative on each side with respect to .

.

Substitute corresponding values in .

Substitute .

Linear approximation: 

Here  and  in above formula.

.