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# 2_3 - lim x → a f x ≤ lim x → a g x Remember m √ t...

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Section 2.3: Calculating Limits Using the Limit Laws Instructor: Ms. Hoa Nguyen Limit Laws Suppose that c is a constant and the limits lim x a f ( x ) and lim x a g ( x ) exist. Then 1) Limit of sum/ diﬀerence = Sum/ Diﬀerence of limits: lim x a [ f ( x ) ± g ( x )] = lim x a f ( x ) ± lim x a g ( x ). 2) Limit of constant times function = constant times limit of function: lim x a [ cf ( x )] = c lim x a f ( x ). 3) Limit of product/ quotient = product/ quotient of limits: lim x a [ f ( x ) · g ( x )] = lim x a f ( x ) · lim x a g ( x ). lim x a f ( x ) g ( x ) = lim x a f ( x ) lim x a g ( x ) if lim x a g ( x ) 6 = 0. 4) Power law: lim x a [ f ( x )] n = [lim x a f ( x )] n where n is a positive integer. 5) Inequality: f ( x ) g ( x ) when x a =
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Unformatted text preview: lim x → a f ( x ) ≤ lim x → a g ( x ). Remember : m √ t = t 1 m (Notice: If m is even, we assume that t > 0). Example 1 of Section 2.3 (textbook): Example 5 of Section 2.3 (textbook): Example 6 of Section 2.3 (textbook): Example 8 of Section 2.3 (textbook): Example 9 of Section 2.3 (textbook): The Squeeze/ Sandwich/ Pinching Theorem f ( x ) ≤ g ( x ) ≤ h ( x ) when x → a and lim x → a f ( x ) = lim x → a h ( x ) = L = ⇒ lim x → a g ( x ) = L . Example 11 of Section 2.3 (textbook): 1...
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