The City College Department of Mathematics
Spring 2010 Ma
Part I
th 20100 Final Exam
(70 points) Answer all questions.
1.
(15pts) Find the deri ative and simplify (write without negative exponents and
factor if possible):
y
=
x
2
sin(
v
a.
b.
3
x
)
f
(
x
)
=
x
+
3
x
2
2
−
c.
y
=
cos
3
(
x
2
+
2)
2.
(15 pts) Compute each of the following integrals and simplify (write without
negative exponents and compute any trig evaluations):
x
a.
+
3
x
2
−
2
⎛
⎝
⎜
⎞
⎠
⎟
∫
dx
b.
()
2
3
3
68
4
x
dx
xx
+
+
∫
Page 1 of 3
c.
3
4
sin(5 )
x dx
π
∫
3.
(6pts) Find
(2)
f
′
as a reduced fraction, where
2
3
5
x
fx
x
x
+
=
−
. (You do not have to
e expression for
simplify th
f
x
′
).
=
2
+
2
4.
(6p
)
ts For
x
y
2
3
+
a.
Find
dy
.
x
2
y
dx
b.
Find the slope of the curve at
(1
,1
)
.
5.
(6pts) Find
n
−
−
the area u der the graph of
y
=
sin
x
over the interval
[ ]
4,
.
,
6.
(7p
)
ts For
f
(
x
)
=
1
x
2
a.
Use the limit definition to find
′
.
b.
Find the equation of the tangent line to
f
(
x
)
at
x
= −
2
.
7.
(7pts) When a circular plate is heated in an oven, its radius increases at the rate of
0.01 cm/min. At what rate is the plate’s area increasing when the radius is 50cm?
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 Fall '14
 Math, Calculus, Exponents, Derivative, Trigraph, FINAL EXAM SPRING, 0.01 cm, 7pts

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