Questions from Calculus


Q: Determine the signs of the partial derivatives for the function f whose

Determine the signs of the partial derivatives for the function f whose graph is shown. (a). fx (21, 2) (b). fy (21, 2)

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Q: Verify that the conclusion of Clairaut’s Theorem holds, that is,

Verify that the conclusion of Clairaut’s Theorem holds, that is, uxy = uyx. u = ln (x + 2y)

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Q: Find the indicated partial derivative(s). f (x

Find the indicated partial derivative(s). f (x, y) = x4y2 - x3y; fxxx, fxyx

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Q: Find the indicated partial derivative(s). g (r

Find the indicated partial derivative(s). g (r, s, t) = er sin (st); grst

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Q: Find the indicated partial derivative(s). /

Find the indicated partial derivative(s).

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Q: Find the indicated partial derivative(s). /

Find the indicated partial derivative(s).

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Q: Find the indicated partial derivative(s). /

Find the indicated partial derivative(s).

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Q: Find the indicated partial derivative(s). /

Find the indicated partial derivative(s).

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Q: A particle has position function r(t). If r'(

A particle has position function r(t). If r'(t) = c × r(t), where c is a constant vector, describe the path of the particle.

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Q: If f and t are twice differentiable functions of a single variable

If f and t are twice differentiable functions of a single variable, show that the function u (x, t) = f (x + at) + t (x – at) is a solution of the wave equation given in Exercise 78. Exercise 78: Sh...

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