View the step-by-step solution to:

Question

Screenshot_20191002-195059_Drive.jpghow to do those?

src="/qa/attachment/10702685/" alt="20191002_195300.jpg" />20191002_195337.jpg

20191002_195300.jpg

7:51 1 0 & vy
ON all 79%
H14pt3.pdf
. .
Math 2415
Homework on 14.3
1. Compute the partial derivatives of, of, off, at, and andy
of the following functions.
(a) f(x,y) = x cos x sin y
(b) f(x,y) = e-(22+y?)/(202)
2. Let f(p, 0, ) = psin ocos 0. Calculate of and of
3. The plane y = 2 intersects the graph of z = ry3 +5x2 in a curve. Find a parametrization
of the tangent line to this curve at the point where x = 3.
df
6.
nbraries/ MW
.pdf
7. Verify that the function u(x, y, z) = log (x2 + y?) is a solution of the two dimensional
Laplace equation uxx + Wyy = 0 everywhere, except of course at the origin where f is
not defined.
8. Verify that the following functions solve the wave equation, Utt = Uzz
(a) u(x, t) = cos(4x) cos(4t)
(b) u(x, t) = f(x -t) + f(x+t), where f is any differentiable function of one variable.
O

20191002_195337.jpg

7:51 6 H C“ at.- El i i i 8 H14pt4.pdf Math 2415
Homework on 14.4 1. Find an equation for the tangent plane to the surface 2 = My 7 1‘ at the point. (as, y, z) =
(1, 2, 1). 2. Let f(1‘,y) : 123,12 7 1'. {3] Find the equation for the tangent plane to the graph of f at (2. l. 2).
(b) Use a linear approximation to find the approximate value of f(1.9, 1.1). 3. Calculate the linearization of the function f at the point P and use it to estimate f (Q)
for {a} z : fishy) : [1r — y) cos(21rsry) where P : (1%) and Q : {1.1.0.4}
. P 6. The period of oscillation of a pendulum of length L is given by the formula T :
27r L/g. Where g is the acceleration due to gravity. Estimate the change in the period
of the pendulum if its length is increased from L = 30 cm to L = 3] cm and it is
simultaneously moved from a location where g = 9.8 m/s2 to one where g = 9.85 m/sz. III C) <

Screenshot_20191002-195059_Drive.jpg

7:50 1 0 & v
Call 79%
H14pt1.pdf
. .
Math 2415
Homework on 14.1
1. Stewart 14.1.44
2. Sketch the level curves f (x, y) = c of the following functions z = f(x, y) at the specified
values of c. Then sketch the graph of f.
(a) f(x, y) = (100 - x2 - 72)1/2, c = 0, 2, 4, 6, 8
(b) f(x, y) = y - x2, c=0, +1, +2.
3. Sketch the level surfaces f(x, y, z) = c of the following functions w = f(x, y, z) at the
specified values of c.
(a) f(x, y, z) = 4x2 + 2 + 922, c = 0, 1, 2.
4. Match the functions z = f(x, y) with the surfaces representing their graphs. Justify
your answers. (The origin is in the middle of each box. The figures only show that
portion of the surface that is inside a box.)
(a) f(x, y) = x2+2
(b) f(x,y) = (x2 - y?) exp(-12 - y?)
(c) f(x, y) = sin(x2 + 2y?)
III
IV
V
VI
VII
VIII
IX
X
1
O

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes