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Unformatted text preview: Name:
TA: PID:
Sec. No: Sec. Time: Math 10A.
Midterm Exam 2
February 28, 2011 Turn oﬀ and put away your cell phone.
You may use one page of notes, but no books or other assistance during this exam.
Read each question carefully, and answer each question completely.
Show all of your work; no credit will be given for unsupported answers.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
If any question is not clear, ask for clariﬁcation. # Points Score 1 9 2 8 3 8 4 8 Σ 41 1. Find the derivatives of the following functions. You do not have to simplify.
(a) (3 points) g (x) = tan2 (3x − π ) 2 ex + x
(b) (3 points) h(x) =
x2 (c) (3 points) f (x) = 2sin(x) cos(x) 2. (8 points) The ﬁgure below gives the position, f (t), of a particle at time t. 8
6 f(t) 4
2 t2 t1 0 t
t4 t3 2
4
6
8 0 1 2 3 4 5 6 7 8 9 At which of the marked values of t can the following statements be true?
(a) The position is positive. (b) The velocity is positive. (c) The position is decreasing. (d) The velocity is increasing. 3. The ﬁgure gives the graphs of functions y = f (x) and y = g (x). 8 y
y=f(x) 6
4 y=g(x) 2
0
x
2
4
6
8
0 1 2 3 Give approximate values for
(a) (1 point) f (x)g (x) at x = 2 (b) (1 point) f ( x)
at x = 4
g (x) (c) (3 points) d
[f (x)g (x)] at x = 1
dx (d) (3 points) d f (x)
at x = 8
dx g (x) 4 5 6 7 8 9 10 4. (a) (4 points) Let g (t) = t2 − t. Use the limit deﬁnition of the derivative to ﬁnd
g (−1). (b) (4 points) If f (x) = 4x3 + 6x2 − 23x + 7, ﬁnd the intervals on which f (x) > 1. ...
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This note was uploaded on 09/07/2011 for the course MATH 10A taught by Professor Arnold during the Fall '07 term at UCSD.
 Fall '07
 Arnold
 Math, Calculus

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