Ace - AI Tutor
Ask Our Educators
Textbooks
My Library
Flashcards
Scribe - AI Notes
Notes & Exams
Download App
James Chan

James C.

Divider

Questions asked

ANSWERED

Uma Kumari verified

Numerade educator

11. For the curve given by ( vec{r}(t)=langlesqrt{2} cos t, sqrt{5} sin t, sqrt{3} cos t angle ), find a. the unit Tangent vector b. the curvature

View Answer
 divider
ANSWERED

Arjun Singh verified

Numerade educator

Find an equation of the plane containing the point (2, 1, 3) and the line x = 1 + 3t, y = -2 - t, z = 3t.

View Answer
 divider
ANSWERED

Uma Kumari verified

Numerade educator

Find the equation of the tangent plane to the surface x^2 + xy + y^2 + z^2 = 16 at the point (1, 2, 3).

View Answer
 divider
ANSWERED

Urvashi Arora verified

Numerade educator

8. Suppose F(x, y, z) = x^4y + y^2z^3, x = rse^t, y = rs^2e^-t, and, z = r^2s sin t a. Find ?F/?t. b. Find ?F/?s when r = 2, s = 1, t = 0.

View Answer
 divider
ANSWERED

Uma Kumari verified

Numerade educator

Find all the critical points of the function f(x, y) = x^3 - 9xy + y^3, and classify each one as local maximum, local minimum, or saddle point.

View Answer
 divider
ANSWERED

William Semus verified

Numerade educator

Find the mass of a thin plate with density function ?(x, y) = y occupying the triangle with vertices (0, 0), (1, 1), and (-1, 1).

View Answer
 divider
ANSWERED

David Nguyen verified

Numerade educator

5. Write an iterated integral in cylindrical coordinates for the region above the cone z = r and below the sphere ? = 2 for z ? 0 in the order d? dz dr. Sketch the region of integration. DO NOT EVALUATE. (9 pts)

View Answer
 divider
INSTANT ANSWER

4. Convert the integral below from cylindrical coordinates to an equivalent integral in a) Rectangular and b) spherical coordinates. Sketch the solid and DO NOT EVALUATE. (9 pts) \[ \int_{0}^{\pi} \int_{0}^{1} \int_{0}^{\sqrt{3} r} r^{2} \sin \theta d z d r d \theta \]

View Answer
 divider
INSTANT ANSWER

3. Use Green's theorem to evaluate \( \oint_{C}\left(y \cos x-e^{-x}-y\right) d x+\left(\sin (x)+x+e^{y}\right) d y \) where \( C \) is the boundary of the region oriented counter-clockwise whose area is \( \frac{\pi}{2}+1 \). (9 pts)

View Answer
 divider
INSTANT ANSWER

2. Given \( \vec{F}(x, y, z)=\left\langle 2 x y-z^{2}, x^{2}+2 z, 2 y-2 x z>\right. \) and a path \( C \) described as: a line segment from point \( A(-3,-2,-1) \) followed by the arch of a cycloid and followed by the top half of a parabola ending at point \( B(1,2,3) \). Evaluate \( \int_{C} \vec{F} \cdot d \vec{r} ;(9 p t s) \)

View Answer
 divider