due in class on Friday, November 8
Student No:
Name (Print):
Note: All homework assignments are due in class one week after being assigned.
They must be on standard 8
1
2
×
11 size paper and they must be stapled. Assign
ments which are not stapled will not be accepted. I will not bring a stapler to
class. Please enter your student number and name (as it appears on the regis
trar’s list) in the spaces above. SURNAME FIRST IN CAPITALS, and given
name second. Please put your answers in the boxes (if provided) and submit
these pages for your assignment.
1. Find the linearizations
L
(
x
) of the following functions
f
(
x
)near
x
=0
.
(a)
f
(
x
)=
√
25 +
x
2
+
x
.
(b)
f
(
x
)=(1

2
x
)
β
,
where
β
is some constant.
(c)
f
(
x
)=ln(
x
+
√
1

x
2
)
.
2. Two towns on the trans Canada Hiway are 100
km
apart. Two cars leave the ﬁrst town at
1:00 pm and both arrive at the second town one hour later. Show that at sometime between
1:00 pm and 2:00 pm they had the same velocity.
1
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 Winter '06
 denissjerve
 Derivative, Inverse trigonometric functions, Convex function, Concave function, Jensen's inequality

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