Question

The approximate value of function f(x + δx, y + δy) is?

(a) f + ^∂f⁄∂x dx + ^∂f⁄∂y dy

(b) ^∂f⁄∂x dx + ^∂f⁄∂y dy

(c) f – ^∂f⁄∂x dx + ^∂f⁄∂y dy

(d) ^∂f⁄∂x dx – ^∂f⁄∂y dy

The question was asked in an interview.

My question is based upon Errors and Approximations in division Partial Differentiation of Engineering Mathematics

Answer 1

The correct option is (a) f + ^∂f⁄∂x dx + ^∂f⁄∂y dy

Explanation: f(x + δx, y + δy) = f(x,y) + df = f + ^∂f⁄∂x dx + ^∂f⁄∂y dy.