1051 Assignment 2
Due Thursday 1st April 2010, 2 pm
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Write your name, student number, tutor’s name, tutorial group (T1, T2, . . . ) and tutorial time clearly on
the top of the front page of your assignment.
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Staple
the pages of your assignment. Locate the box on level 3 of building 67 corresponding to your tutorial
group. Place your assignment there by the indicated deadline.
Late assignments will not be accepted.
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Write your answers clearly. Illegible assignments will not be marked.
?
Show all your working. Correct answers without justification will not receive full marks.
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Hand in only the questions marked by
boxes
: # 2(ii), 3, 4(iv), 6, 7.
Question 1.
For
x >
0 solve
2 ln(
x
3
)

ln(32
x
) = ln 4
.
Question 2.
Evaluate the following limits:
(i) lim
x
→
3
(
x
2

3
x
+ 2) ,
(ii)
lim
x
→
2
x

2
√
x

√
2
,
(iii)
lim
x
→∞
(3
x

1)(3
x
+ 3)
(5
x

3)(4
x
+ 5)
,
(iv)
lim
x
→∞
3
x
x

1

2
x
x
+ 1
.
Question 3.
Find the inverses of the following functions:
(i)
f
(
x
) =
x
x
+ 2
,
(ii)
f
(
x
) = cos
π
√
x
+ 1
.
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