Multivariable calculus quiz

Five questions on Multivariable calculus. Answer all 5 to see your score.

0 of 5 answered

Question 1 of 5

For u = \langle 2, -1, 3 \rangle and v = \langle 1, 4, -2 \rangle, compute the dot product u \cdot v.

Compute the cross product u \times v for u = \langle 2, 1, 0 \rangle and v = \langle 1, 3, 0 \rangle.

For f(x, y) = x^2 y + \sin(xy), what is the partial derivative \frac{\partial f}{\partial x}?

For f(x, y) = x^2 + y^2, find the directional derivative at the point (1, 2) in the direction from (1, 2) toward (3, 4).

Evaluate the double integral \int_0^1 \int_0^2 (x + y) \, dy \, dx.