Question

(a) Evaluate f (2, 1) and f (2.1, 1.05) and calculate Δz, and (b) use the total differential dz to approximate Δz.

Answer 1

(a)

Step 1:

The function is .

Evaluate .

Substitute in .

.

Evaluate .

Substitute in .

.

Formula for .

Substitute and .

.

Solution:

, and .

Answer 2

Contd...

(b)

Step 1:

The function is .

If and are increments of and , then the differentials of the independent variables and are and .

The total differential of the dependent variable is .

Find and .

Apply partial derivative on each side with respect to .

.

Apply partial derivative on each side with respect to .

.

Substitute , , and in .

.

Solution:

.