MATH 241 Study Guide - Midterm Guide: Tangent Space, Cylindrical Coordinate System, Directional Derivative

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turquoisegnu128

10 Jan 2019

School

University of Maryland

Department

Mathematics

Course

MATH 241

Professor

ALL

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Math 241h - exam 1 - oct. 16, 2002 (8) 1. What type of surface does this equation de ne? (b) translate = /2 from spherical into standard (x, y, z) coordinates. What type of surface does this equation de ne? (20) 3. Let f (x, y) = (cid:26) xy x2+y2. Find duf (0, 0) or explain why it doesn"t exist. (21) 4. Suppose that f : r2 r2 is given by f (x, y) = (xy, x2 y2) and that g : r2 r2 satis es g(2, 1) = (1, 3) and. 2 (a) find the derivative matrix df (x, y). (b) find the derivative matrix d(f g)(2, 1). (22) 6.

Related Questions

1) Show that the follwing limit does not exist

lim_(x,y)-(0,0)(xy+x²)/(x^²+y²)

2) Fin all the second orderpartial derivatives of

f(x,y,z)=x²tan^-1(y+z)

3) Find the equation of thetangent plane to the surface

z=x²-4y² atthe piont (1,2,-15).

4) Fin the linear approximation tothe function

f(x,y,z)=e^-2xy+cos(2yz) at the point (1,-1,2)

5) Fin the normal vector to thesurface

z²=x²-y² at the point (5,3,4)

6) You are standing on a surfacegiven by the equation

z=x^2-2y². Ifyou are standing at the poin (2,1,0), in which directio is thesteepest slope?

7) The temperature in the solarsystem is given by

T(x,y,z)=10⁵/(x²+y²+z²). If acomet travels along the path r(t)=(t, t²-4, 2t), howfast is the temperatur changing when t=2?

8) Fin the critical point of thefunction f(x,y)= e^4x-e^-y. Use the secondderivative test to classifyf them, if possible.

9) Fin the extreme values off(x,y)=4x2+3y2 on the square 0 is less than or equal x,y less thanor equal to 1.

ceruleancockroach23

Calc 4 review! I need help with any of all of them!

MATH 241 Study Guide - Midterm Guide: Tangent Space, Cylindrical Coordinate System, Directional Derivative

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