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Math 1634 Calculus I
June 22, 2009
Test No.2
NAME: __ ~OL.':'T;~ ________ _
(please print)
Prof. Guy Bernard
There are seven problems worth a total of 100 points.
Calculators are allowed during this test, but you must show your calculations in all
problems. No books or notes are allowed during this test.
No.1 (15 pOints) Evaluate the derivatives of the following functions.
You must show the details of your calculations.
a) f(x) = (In x)'
b) g(x) = arcsin(3x)
J I _ '1,.:."l
."' .. , ,, *~
~ I ("" _ ~.) 5" ( 2'0< ... "3)
page 2
No.2 (15 points) Find the slope of the tangent line to the curve
at the point P{I,·I).
Hint: Do not try to solve the equation for y = y(x).
Use Implicit Differention instead.
\(4"", .... ,..1.
,
,><~+'2."d
=
d
'4 ~'t(7'1
':t~
.,.
... '2." b
=
";}" h
,+..,.. 4 2d
d",
d,...
5~""SI
'f
_ '"2. + '2~

'3 ~ '"
~ _ I
C!,..
"2
I
'2J~
= " J:t
d..<
d ;'<
~
page 3
No.3 (15 points) Find ...
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