Allied & ICAR Exam Bank • ALLIED_0032 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Total differentiation

Question Statement:

If $z = x^2 y$, with $x = 2$ and $y = 3$, and changes are $\Delta x = 0.1$ and $\Delta y = -0.2$, the approximate change $\Delta z$ via differentials is:

Answer Key:

0.4

Step-by-Step Solution & Explanation

$dz = \frac{\partial z}{\partial x} dx + \frac{\partial z}{\partial y} dy = (2xy) dx + (x^2) dy = (2 \times 2 \times 3)(0.1) + (4)(-0.2) = 1.2 - 0.8 = 0.4$.
← Previous (ALLIED_0031) Next (ALLIED_0033) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test