MID TERM #2, MATH 100
Wednesday, November 13, 2002
Student No:
Name (Print):
There are 5 pages to this test, check to make sure it is complete.
Please put your name
and student number at the top of every page.
Rough work should be done on the backs
of the pages, and
your answers put in the boxes (if provided). You must show all
your work to get full marks. Calculators and notes of any kind are not allowed.
1. [6 marks]
(a) Find the derivative of
f
(
x
)=arcs
in(
√
x
)
.
Do not simplify.
(b) Find
f
0
(
x
)
f
(
x
)
if
f
(
x
)=(
ln
x
)
x
and simplify.
(c) Find
f
0
(
x
) for
f
(
x
) = arctan
±
x

1
x
+1
²
and simplify.
Please do not write in this space.
Number
Value
Grade
Question 1
6
Question 2
8
Question 3
12
Question 4
12
Question 5
12
Total
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Student No:
Name (Print):
2. [8 marks] Let
f
(
x
) be the function
f
(
x
)=
x
(ln
x
)
2
,x>
0
.
(a) Find all
x
where
f
0
(
x
)=0
.
(b) Find all
x
where
f
00
(
x
)=0
.
(c) Find all intervals where
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 Winter '06
 denissjerve
 Statistics, Approximation, Simmering

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