MATH 241 Midterm: MATH241H_HERB-R_FALL2003_0101_MID_SOL

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turquoisegnu128

10 Jan 2019

School

University of Maryland

Department

Mathematics

Course

MATH 241

Professor

ALL

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To get a normal vector we take n = a b = ( 2, 7, 3). Thus the equation is 2(x 3) + 7(y + 2) 3(z 0) = 0: (a) plug in to get f (1, 0) = 2. (b) doesn"t exist because limits are di erent from di erent directions. For example limx 0 f (x, 0) = 2 and limy 0 f (0, y) = 3. (c) no because limit does not exist. (d) f (x, 0) = 2 if x 6= 0 and f (0, 0) = 3. 2x y2 2xy (b) d(f g)(3, 1) = df (2, 1)dg(3, 1) = .

Related Questions

3. (18 pts) Show your work. Let f be a function defined by f(x) = x12 (a) Write the form of the limit and evaluate the limit. Do not use L'Hôpital's Rule. Show your work. 12 12 - 40=(0) - -= lim - 2 = * + 2) = Lima (68–1672 - FORM: (b) Find the natural) domain off. Write your answer in interval notation. (-0, -2) (-2, +00) (c) Let f-1 be an inverse of f. Find an expression for f-1(x), for x in the domain of f-1. = y(x + 2) = 12 yx + 2y = 12 = xy = 12 - 2y = 12 - 2y x= -- x= 12 - 2, and by switching x and y, we get y= 12 - 2 f(x) = 12 (d) Find the value or say "does not exist" (DNE). 1.84(f(n)) = 1 ii. f(p-10)) = DNE, because 0 is not in the domain of f-1

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.

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MATH 241 Midterm: MATH241H_HERB-R_FALL2003_0101_MID_SOL

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