Math 16C Final, Spring 2002 1) For each series, i) Determine if it converges. ii) Justify your reasoning. iii) Find the sum, if possible. a)
(3 points each)
n
n =0
(2.1)n
n!
b)
(0.4 )
n =1
c)
n( n )
n =1 4
1
d)
n 1 n n =1
2) Find the Taylor series for f
MAT 16A (A001)
NAME:
Final Exam
Problem 1. (estimated time: 15mn ) (20 points) Find the derivatives of the following functions. 1. f1 (x) = x3 2x2 + x 1 x3 + 1 (x 1)2 x2 + x 1 3 2
2.
f2 (x) =
3.
f3 (x) =
4.
f (x) =
3
(x2 x 1)2
5.
f5 (x) = cos(2x + 1) x si
16C Final - Fall 2002 1. Find the general solution of the dierential equation x2 y 2xy = 9. 2. The rate of increase in sales S (in thousands of units) of palm pilots is proportional to the current level of sales and inversely proportional to the square of
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Math 16A Short Calculus
Final Exam
Name: Signature:
Directions: Turn o all cell phones now. Do not open your test until directed. You may not use books, notes, calculators, or cell phones on this test. Read each problem carefully. Make sure you answer eve
MAT 16A (A002) March 20, 2003
NAME:
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4
total
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Problem 1. (estimated time: 25mn ) (50 points) (a) Which of the following lines are parallel? Which of them are perpendicular? 1 1 3 L1 : x y + 1 = 0 L2 : y = x + 5 L3 : x 3y + 3 = 0 3 2 2 L4 pass