Math 1910 Prelim I,
7:309pm, September 29, 2011
Answer the following 5 questions.
Show all work.
Closed book, no calculators; 1sided (8.5 x
11) “cheat sheet” is allowed – individually and uniquely handwritten (without collaboration) –
will be collected along with the exams – will not be returned.
Academic integrity on the part of
each student is presumed
.
Violations will be dealt with swiftly and justly.
1. (a) Solve
2
cos( )
.
[sin( ) 99]
x
dx
x
−
∫
(10pts)
(b) Find the function
( ),
fx
defined for
2,
x
<
such that:
(i) at any point
(, )
xy
on the curve
( ),
y fx
=
the slope of the tangent to the curve is given by
2
1
,
(
2)
x
−
and (ii) the point
(1,7) lies on the curve. (15pts)
2. Determine the constant
1
a
>
such that the area under the curve
1
y
x
=
between
1 and
x
xa
=
is equal to 2. (15pts)
3. Consider the function
3
42
( )
2
, for 1
3:
x
f x
t
t dt
x
≡
+
≤≤
∫
(a)
Find
( ).
′
(10pts)
(b) Are there any critical points, i.e., points
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This note was uploaded on 10/31/2011 for the course MATH 1910 at Cornell.
 '07
 BERMAN
 Math, Calculus

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