Calculus I (MAT 145) Dr. Day Friday January 25, 2019

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Presentation transcript:

Calculus I (MAT 145) Dr. Day Friday January 25, 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! Quiz #2/3 today! Friday, Feb 1: Test #1 in STV 346 Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

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). Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

Vertical Asymptotes Friday, January 25, 2019 MAT 145

Limits and Vertical Asymptotes Use limit statements to describe the vertical asymptotes. Friday, January 25, 2019 MAT 145

LIMIT LAWS! Suppose that c is a constant and the limits and exist. Friday, January 25, 2019 MAT 145

MORE LIMIT LAWS! Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

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: Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

Friday, January 25, 2019 MAT 145

by finding its intercepts and its limits as and as . Sketch the graph of by finding its intercepts and its limits as and as . Friday, January 25, 2019 MAT 145