Solution. First, we need the derivative: r0(t) = h3t1/2, −2 sin(2t), 2 cos(2t)i. Next, we integrate the magnitude: L = Z 1. 0. |r0(t)| ...

You need to convert the region into uv coordinates. (6 points), you need to convert the function into uv coordinates (4 points), and then you need a Jacobian. ( ...

Let C be the intersection of the sphere of radius 2 centered at the origin and the plane y + z = 0. (a) (5 points) Write parametric equations for C. (b) (5 ...

Practice Midterm 2. No electronic devices (laptops, calculators, telephones) or notes are al- lowed during exams. Numerical expressions involving square ...

Fundamentals of Differential Equations · 1) find the critical points of the function by taking the partial derivs of each variable and setting to 0. · 2) then ...

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(1) You are standing on a surface given by the equation z = 4x2 − 2xy − y2. If you're standing at the point (1,2,−4), in which direction is the fastest way up?

This examination booklet contains 5 problems, including one bonus problem, on 7 sheets of paper including the front cover. Please detach the last page before ...

MAT203 Calculus III. Midterm Exam 2. 11/8/2019. In Memory of Felix Hausdorff (November 8, 1868 - January 26, 1942). Problem. Points. Problem 1 ...

Directional vector is vector pointing in direction of max rate of increase (from a) times new vector after dividing by magnitude.