MAT135Y – 20072008
Review Problems for TermTest 2
The following problems were given at second termtests of previous academic years. For each
problem there is a year followed by a number. The year is the year at which the problem was given
and the number is the number of the problem in the TermTest 2 booklet of that year. For instance
[‘03, 6] refers to Problem 6 of TermTest 2 of December 2003.
You can get the answers of the
problem by looking at the solutions of the corresponding termtest. These solutions are available
online at:
http://www.math.utoronto.ca/ponge/teaching/200708/MAT135/MAT135.html
.
The sign
?
indicates that the problem is chalenging.
Problem on Chapter 2
Problem 1
(‘03, 6)
.
Let
f
(
x
) =
sin
kx
sin 2
x
if
x <
0
,
(
x
+
k
)
2
+ (5
k
+ 2)(
x
+
1
2
)
if
x
≥
0
.
Find the value of the constant
k
so that
f
is continuous everywhere.
(a) 0
(b) 2
(c)

1
(d)
5
2
(e)
1
2
.
Problems on Chapter 3
Problem 2
(‘03, 7)
.
The line tangent to the curve
x
2
+ 3
y
2
= 1 at the point (
1
2
,
1
2
) intercept the
y
axis at the point
Problem
?
3
(‘02, 18)
.
Let
f
(
n
)
(
a
) denote the
n
’th derivative of
f
at
a
. If
f
(
x
) =
e
2
x
cosh(2
x
) sinh(4
x
),
then
f
(20)
(ln 4) =?.
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 Spring '08
 LAM
 Derivative, Mathematical analysis, Convex function

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