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 practicing
this process.
Example 1. Consider the function f
Part A: Quick Answer 15 marks
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Part A: Quick Answer 15 marks
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mark.
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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. This concept is a critical one that
the rest of the cour
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)
dx
2
5
Z (x + 2)
(v)
(ix)
(x)
Z
(2x + 1)ex
2 +x
dx
ex
d
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.
Feel free to write in pencil or pen.
Non-programmable
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 Kaidan is 1.7 m tall, how long is his shadow?
2
(b) Kaid
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, reverse exponential,
reverse log, etc.). Lets warm up wi
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
different from those that we looked at in class.
x3 + 8
.
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 approximation to estimate the value
of ln(1.1).
x3
. Dete
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 f decreasing?
(c) Which of the value(s) in (b) corresp
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 definition to find the deriva1
.
tive of f (x) =
x1
A
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.
Example 1. (a) Find all values of x satisfying
using the c
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 the following. Are you
comfortable with:
_ Basic rules
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 formal definition of the limit
lim (3ex 1) = 1
x
Exampl
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), if x, y > 0
x
(iv) loga
= loga(x)
y
loga(y), if x,
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, though, Maple TA needs to be able to
understand what you mea
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 on x and y,
but cannot be solved for x or y). Here is an