GATE · Engineering Mathematics
Differentiation
18 practice questions, each with the answer and an explanation.
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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.
All 18 questions
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- What is the directional derivative of the scalar field f(x, y, z) = x^2 y + y^2 z + z^2 x at the point (1, 1, 1) in the direction of the unit vector u = (1/√3, 1/√3, 1/√3)?
- Evaluate the limit: L = lim_(x -> 0) [x - sin(x)] / [x^3].
- At what point does the function f(x, y) = x^3 + y^3 - 3xy achieve a local minimum?
- For the vector field F = (y^2) i + (2xy + z) j + (y) k, what is the value of curl(F) at any point (x, y, z)?
- If u(x, y) = e^x cos(y) is the real part of an analytic function f(z) = u + i v, what is the harmonic conjugate v(x, y) satisfying v(0, 0) = 0?
- What is the maximum value of the function f(x, y) = x y subject to the constraint x^2 + y^2 = 8?
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