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2311lectureoutline2.2

# 2311lectureoutline2.2 - the limit will equal the value of...

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MAC2311, Calculus I 2.2 The Limit of a Function Definition of a Limit: If f(x) becomes arbitrarily close to a unique number L as x approaches a from both sides, then we say the limit of f(x), as x approaches a, is L, and we write ( ) lim x a f x L = . Find limits graphically. The two most common types of problems where the limit does not exist… f(x) approaches a different value from the right of a than from the left. f(x) increases or decreases without bound as x approaches a. Note: The limit of f(x) as x approaches a does not depend on the value of f(x) at a. But sometimes we can use direct substitution and
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Unformatted text preview: the limit will equal the value of f(x) at a. These are called “well-behaved” functions and are said to be “continuous” at a. One-sided Limits: ( ) lim x a f x L + → = means “the limit of the function f(x) as x approaches a from the right is L.” ( ) lim x a f x L-→ = means “the limit of the function f(x) as x approaches a from the left is L.” Note: The ( ) lim x a f x L → = if and only if ( ) lim x a f x L + → = = ( ) lim x a f x L-→ = . Examples: Try exercises 2,8,26,28 on page 96 in the text. Try exercise 6 with a partner....
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