Apr. 24, 2014
Math 200
Name:
Page 2 of 15 pages
Formulas
Projection of v onto u:
proju v =
uv
u.
uu
Cross product
a, b, c d, e, f = bf ce, (af cd), ae bd .
Equations of the line through (x0 , y0 , z0 ) in the direction v = a, b, c :
(x, y, z) = (x0 + t
1. [17] Consider the surface given by: z 3 xyz 2 4x 0. z z (a) Find expressions for x , y as functions of x, y, z. z z (b) Evaluate x , y at 1, 1, 2. (c) Measurements are made with errors, so that x 1 0. 03 and y 1 0. 02. Find the corresponding maximum er
r
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MATH 253 SEC LA4 W2O11T1
Quiz no. 1
2:O02:20pmo Sep 20, ZOLL
Student I.D. Number:
Signature:

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INSTRUCTIONS: This is a closedbook exam. You may not use any books, notes,
papers, calculators, or other aids. Do all work on the sheets provided. T
Some Review Problems
Here are some dierentiation and integration problems. You should also review your notes from the rst two calculus courses. Please email me if you nd any errors in the solutions. QUESTIONS 1. Find the derivative of f (x) = sin(x2 + x)