MATH 10A Bonus Assignment
Name
(Section B0
)
Due February 9, 3:50pm in class.
This assignment is worth up to 3 points on your Midterm 1 score. You may get help
with these problems, but the solution should be written by you in your own words.
Ex
plain your solution clearly. You are encouraged to use the midterm solutions as a guide.
Problem 1:
Find
k
so that the function
f
(
x
) =
(
x
+
k, x
≤
5
kx,
5
< x
is continuous on any interval.
Solution:
Each piece of
f
is continuous. To make
f
continuous on any interval, we
need in particular, to make the left and right hand limits agree at
x
= 5, and actually
be equal to
f
(5).
So we must solve
5 +
k
=
f
(5) = lim
x
→
5
+
f
(
x
) = lim
x
→
5
+
kx
= 5
k,
which gives
k
=
5
4
.
Problem 2:
For the function
f
(
x
) =

2
x

6

x

3
, ﬁnd
lim
x
→
3
+
f
(
x
)
,
lim
x
→
3

f
(
x
)
, and
lim
x
→
3
f
(
x
)
.
Solution 1 (the graphical way):
To obtain the graph of
f
(
x
), start with

x

x
, translate
it 3 units to the right, and stretch it vertically by a factor of 2 to get
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 Winter '07
 Arnold
 Math, ... ..., Graph of a function

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