Allied & ICAR Exam Bank • ALLIED_2640 NAT • 2 Marks

Section 1: Engineering Mathematics

Calculus

Subtopic: Total differentiation

Question Statement:

If $z = x^3 y^2$, and $x$ increases by $2\%$ while $y$ decreases by $1\%$, the percentage change in $z$ using total differentials is:

Answer Key:

4

Step-by-Step Solution & Explanation

Taking logarithmic differentials: $\frac{dz}{z} = 3 \frac{dx}{x} + 2 \frac{dy}{y} = 3(+2\%) + 2(-1\%) = 6\% - 2\% = 4\%$.
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