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GATE 2017 CE (CE2) – Question 29

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 1 mark · Numerical answer

The divergence of $\mathbf V=x^2\hat i+2y^3\hat j+z^4\hat k$ at (1,2,3) is ______.

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Correct answer: 133.9 to 134.1

Explanation

Differentiate each component with respect to its matching coordinate: $\nabla\cdot\mathbf V=2x+6y^2+4z^3$. At (1,2,3), this is $2+24+108=134$.