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2 Inverse Functions
2.1 Introduction
Suppose that f is a function with a (1m of X and 5.
Isaac. of Y. (We sometimes write f : X > Y.) Then, the
inverse function is a function f"1 : Y + X suc
[email protected]
1 An Introduction to Complex Numbers
1.1 Introduction
We are familiar with quadratic functions of the form
f(a:) = @532 + 633+ c,
Where a, b, and c are PEAJ_ rim . Such functions, as we
saw in high school math, may be re
@311 When we nd the v we dont need to worry about including
+0. Why not?
Example 2. Integrate: / tsecgt) dt -"-'- 5 f (39) fl cfw_M (2*) 0H7
Lel' u. = t - mt)
We can use the integration by parts formula creatively to nd some
interesting antiderivatives:
2.4 Derivatives and Antiderivatives Involving Arctrig Functions
Weve introduced six new functions. With new functions come new
d ark/05mg fwxotiovxS !
Example 8. Use implicit dierentiation and the Pythagorean
theorem to nd the derivative of the function y
4 LHpitals Rule
ln MATH*1200 we studied limits extensively. We return now to the
0
discussion of 5 limits and the notion of an indeterminate form.
4.1 Indeterminate Forms
0
Indeterminate forms refer to results such as _Q when we try to
j _u;i_ p_lt%_ iJLL
How to integrate by direct
substitution
EXTRA MATERIAL FOR MATH 1210
Step 1
An integral is given to you to compute, such as:
2
dx
3
2 +
Step 1
An integral is given to you to compute, such as:
2
dx
3
2 +
A substitution should make our lives easier,
MATH 1210 Calculus II
Lab Problems - Winter 2013
Dr. Monica-Gabriela COJOCARU
Associate Professor of Mathematics
Department of Mathematics and Statistics, University of Guelph
March 7, 2013
2
Copyright c Monica-Gabriela Cojocaru 2013
Textbook:
Calculus 7e