Lab 11
This week we extended our discussion of antiderivatives to include
definite integrals. To motivate this, we discussed the Riemann sum
for approximating the area under a curve. We begin by pract
Part A: Quick Answer 15 marks
For each of the following, please ll in your nal answer in the box
provided at the right side of the page. Each correct answer is worth 1
mark.
A1. Solve formif 2S 3m+15.
Part A: Quick Answer 15 marks
For each of the following, please ll in your nal answer in the box
provided at the right side of the page. Each correct answer is worth 1
mark.
A1. True or False: If f is
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3.1 Basic Limits
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3 Limits and Continuity
We now start a deeper discussion of functions, beginning with the
very important topic of limits. T
1
Practice March 20
a) Integrate
(i)
(ii)
Z
(iii)
(iv)
Z
Z
Z
Z
2x
dx
+8
4x
dx
2
x +8
x
dx
x2 + 8
1
x2 ( x3 2)7 dx
3
x2
4x3 (x4 + 1)99 dx
Z
p
(vi)
ex ex 10 dx
Z
1
(vii)
(ln(x) + 1)7/5 dx
Z x
2x
(viii)
1
Midterm Test #3
Math*1200, Fall 2013
Friday, November 15
Last Name:
First Name:
ID Number:
Instructions:
Ensure that your name and ID Number are clearly printed on the front and back
of the test.
1
Lab 1 Sine Law and Cosine Law Examples
1. (a) Kaidan is going for an evening stroll in a flat pasture. The sun
is getting low in the sky, at an angle of 35 degrees inclined from the
horizontal. If K
Lab 10
This week we introduced you to the notion of the antiderivative; that
is, the inverse operation to differentiation. We talked about a variety
of basic rules (reverse power rule, reverse trig, r
Lab 4
This week in class, weve been working on how to solve limits of
0
indeterminate forms such as or if we try to just plug
0
in. Here we have a look at a few examples that are just a little bit
dif
Lab 9
This week we have been dealing with some applications of derivatives!
To help you practice some of these concepts, we present a few extra
examples and discussions.
Example 1. Use differential ap
Lab 8
Example 1. Suppose that a function f (x) has a derivative given
by
3
(x
2)
4x
0
f (x) =
(x 1)2(x 10)
(a) On what interval(s) is the function f increasing?
(b) On what interval(s) is the function
Lab 6
We have just started to talk about derivatives in class this week. In
particular, using the first principles definition of the limit to calculate
derivatives,
Example 1. Use the first principles
Lab 3
Over the past week, we have explored a few different ways to solve
inequalities. Today, well show you that for many problems, there
may be more than one way to find your way to the solution.
Exa
Warm-Up Quiz Checklist
There will already be a test on Friday September 19 on many topics
that you should be familiar with from courses you took back in high
school! Make sure that you practice all of
Lab 5
Example 1. Prove, using the formal definition of a limit, that
lim (4 3x x2) = 6
x2
Example 2. Prove, using the formal definition of a limit, that
lim 3
x1
2
3x 1
2
=2
Example 3. Write out the
Lab 2
In class this week we have been working on (among other things)
logarithmic functions. We presented a number of logarithmic rules
including the following three:
(iii) loga(xy) = loga(x) + loga(y
Your Guide to the Maple TA Mini-Quizzes
Maple TA is a powerful tool, and provides a great opportunity for
you to practice with some of the fundamental concepts of this
course. To make this work, thoug
Lab 7
This week we have been talking about derivative rules (the basics,
product, quotient and chain). We then used these rules to find derivatives of implicitly defined equations (those that depend o