MATH1020 Past Exam Questions
Calculus
For the last three lectures, Oreste went through some solutions to past exams. I actually wasn't at UNI
for the last week (except on Monday), so I have had to borrow notes from Gareth, I'm fairly confident
that Gareth's note taking ability is above average, so it should be OK.
Also thanks to Gareth for lending them to me.
I'm going to put all the questions in this one document because Gareth doesn't have dates in his notes
and they all sort of merge together. Yeah.
From Gareth's notes it seems that Oreste just outlined the way to solve some of the questions without
going into detail, I'll try stay as true to Gareth's notes as I can.
All these questions can be found on the MATH1020 page under “Exercises & Solutions”, it's titled
“Past Exam Questions”.
Also there will be no sketching in the exam! Hooray! I hate sketching...
Semester 1 2008
1.
a) By the extreme value theorem.
b)
f '
x
=
1
−
2cos
x
f '
x
=
0
⇒
cos
x
=
1
2
⇒
x
=
±
3
Now test
−
,
−
3
,
3
,
to find the global and local max/min (first part solved).
Now test the intervals:
x
∈
[
−
,
−
3
3
]
, f '
x
0
x
∈
[
−
3
3
,
3
−
3
]
, f '
x
0
x
∈
[
3
−
3
,
]
,
f '
x
0
From which we can tell where
f
is increasing and decreasing (second part solved).
We can use the intermediate value theorem to show that there is only one point between each
local max and min (and hence there are only 3 points in total) (last part solved).
c)
f ' '
x
=
2sin
x
Concave up between
[
0,
]
concave down between
[−
,
0
]
Point of inflection at 0.
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d)
x
n
1
=
x
n
−
f
x
n
f '
x
n
x
1
=
3
4
−
3
4
−
2sin
3
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 Spring '08
 Hodges
 Calculus, Mean Value Theorem, Limit of a function, Convex function, Rolle's theorem

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