Name: TA Name: Math 20C. Midterm Exam 1 April 28, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit w
Name: Math 20C. Midterm Exam 2 July 23, 2004
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers.
Name: Math 20C. Midterm Exam 2 July 23, 2004
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers.
UCSD 20052006 Spring
Math 20C Calculus & Analytic Geometry For Science & Engineering
Formulae for the rst mid-term examination
For a = a1 i + a2 j + a3 k and b = b1 i + b2 j + b3 k, ab= a2 a3 aa aa i
Quiz 1 Solution for MATH 20C, 2009
1. For R = (1, 4, 3), nd the point P such that v = P R has components < 3, 2, 3 > and sketch v. Ans. Let P = (a, b, c). Then v = P R =< 1 a, 4 b, 3 c >=< 3, 2, 3 >
Quiz 2 Solution for MATH 20C, 2009
1. Consider three points P = (1, 1, 5), Q = (3, 4, 3), R = (1, 5, 7) in three space. (a) Use the cross product to nd the area of the triangle with vertices P , Q and
Solution of Quiz 3 for MATH 20C, 2009
1. Describe the domain and the range of the function f (x, y, z ) = Ans. Domain of f = cfw_(x, y, z )|9 x2 y 2 z 2 0 = cfw_(x, y, z )|x2 + y 2 + z 2 9 which is th
Quiz 4 Solution for MATH 20C, 2009
1. Evaluate the limit or determine that the limit does not exist. y2 (x,y )(0,0) x2 + y 2 lim Ans. We choose two dierent path approaching (0, 0) and nd that there ex
Quiz 5 Solution for MATH 20C, 2009
1. Let f (x, y ) = xex
2 y
and P = (1, 1). fP . , xex
2 y
(a) Find the rate of change of f in the direction of Ans. f =< ex and at P = (1, 1), f (P ) =< 3, 1 >. D
f
Quiz 6 Solution for MATH 20C, 2009
1. Let f (x, y ) = ex xey . (a) Find the critical points of the function f . Ans. fx = ex ey = 0 ex = ey , or x = y, x=0 fy = xey = 0
By solving two equations x = y
Quiz 7 Solution for MATH 20C, 2009
1. For the following double integral, (a) sketch the region and (b) change the order of integration and evaluate.
1 0 y 1
sin x dxdy x
Ans. (b) The domain of integra
Review Solution for Midterm II, MATH 20C, 2009
1
Chapter 13
1. A parking ramp follows the curve in space traced by the function r(t) =< cos t, sin t, t > What is the curvature function (t) of the ramp
Review with Solution for Midterm I, MATH 20C, 2009
1
Chapter 12.
1. [12.2] Find an equation of a sphere if one of its diameters has end-points (2, 1, 4) and (4, 3, 10). Ans. The center of the sphere i
Extra Homework on 14.7 and 14.8
Section 14.7 1. Find the points on the plane x y + z = 4 that is closest to the point (1, 2, 3). 2. Find three positive numbers whose sum is 100 and whose product is a
Print Name: TA Name: Math 20C. Midterm Exam 2 May 26, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no cred
Print Name: TA Name: Math 20C. Midterm Exam 2 May 26, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no cred
Name: TA: Math 20C. Midterm Exam 1 April 25, 2007 Sec. No:
PID: Sec. Time:
Turn o and put away your cell phone. You may use any type of handheld calculator; no other devices are allowed on this exam.
Name: TA: Math 20C. Midterm Exam 2 May 23, 2007 Sec. No:
PID: Sec. Time:
Turn o and put away your cell phone. You may use any type of handheld calculator; no other devices are allowed on this exam. Yo
Mathematics 20C Spring 2009 Name: ID:
Test 1 Section:
Be sure to show all work. Answers without full justication are worth no credit. Remember that you can often check your answers. You may use a sing
Mathematics 20C Spring 2009 Name: ID:
Test 2 Section:
Be sure to show all work. Answers without full justication are worth no credit. Remember that you can often check your answers. You may use a sing
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Print Name: Math 20C. Midterm Exam 1 October 17, 2005
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported
Print Name: Math 20C. Midterm Exam 1 October 17, 2005
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported
Name: TA Name: Math 20C. Midterm Exam 1 April 28, 2006
Section Number: Section Time:
No calculators or any other devices are allowed on this exam. Write your solutions clearly and legibly; no credit w
Name: Math 20C. Midterm Exam 1 July 9, 2004
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. W
Name: Math 20C. Midterm Exam 1 July 9, 2004
Student Number:
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given for unsupported answers. W
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Print Name:
Student Number: Section Time:
Math 20C. Midterm Exam 2 November 21, 2005
Read each question carefully, and answer each question completely. Show all of your work. No credit will be given f