1. Calculus I (MAT 145) Dr. Day Monday January 28, 2019
Approachment  Limits!
Techniques for Determining the Value of a Limit
Numerical Approximation: Same process we used last week
Graphical Approximation: Visual determination
Algebraic Representation: Determining an exact value!
Conjugates
Common Denominators
Expand, Factor, Reduce
Quiz #2/3 today!
Date Change for Test #1: Friday, Feb 8
Monday, January 28, 2019
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2. Monday, January 28, 2019
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3. the function exists at a.
When limit exists
If and , then
If the left-hand limit exists and the right-hand limit exists and they are the same value, then the overall (two-sided) limit exists.
Limits can exist
whether or not
the function exists at a.
And, if the function does exist, but is not the same value as the limit at a (i.e., f(a)≠L), that’s okay, and, in fact, that’s how we know that a function is discontinuous at x=a (stay tuned: Section 2.6).
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6. Vertical Asymptotes
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7. Limits and Vertical Asymptotes
Use limit statements to describe the vertical asymptotes.
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8. LIMIT LAWS! Suppose that c is a constant and the limits and exist.
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9. MORE LIMIT LAWS!
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12. of the curve y = f(x) if either:
The line y = L is called a
horizontal asymptote
of the curve y = f(x) if either:
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17. by finding its intercepts and its limits as and as .
Sketch the graph of
by finding its intercepts and its limits
as and as
Monday, January 28, 2019
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