# L07 - L7 Limit Laws and Denition Suppose c is a constant...

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L7 – Limit Laws and Definition Suppose c is a constant and lim x a f ( x ) and lim x a g ( x ) exist, then 1. lim x a [ f ( x ) ± g ( x ) ] = 2. lim x a c f ( x ) = 3. lim x a f ( x ) g ( x ) = 4. lim x a f ( x ) g ( x ) = 5. lim x a [ f ( x ) ] n = 6. lim x a c = 7. lim x a x = 8. lim x a x n = 9. lim x a x 1 n = 10. lim x a ( f ( x ) ) 1 n = 1

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Evaluate the following limits: 1. lim x →- 1 3 x 2 - 2 x + 5 = 2. lim x 1 x 2 - 3 x + 1 = 3. lim x →- 1 x 3 + 1 x + 1 = 2
4. lim x 0 x (3 - 2 x ) = 5. lim x 8 1 x 1 3 - 2 = 6. lim x 3 x - 12 - x x - 3 = 7. lim x 4 1 x - 4 x 2 4 - x = 3

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8. lim x 0 x 2 + 2 x | x | = Thm – lim x a f ( x ) = L if and only if 4
f ( x ) = 5 - x x 1 x 2 + 1 x > 1 Find lim x 1 f ( x ) . Sketch f ( x ). 5

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g ( x ) = x x ≤ - 1 x 2 - 1 - 1 < x < 2 3 x 2 lim x →- 1 - g ( x ) = lim x →- 1 + g ( x ) = lim x 2 - g ( x ) = lim x →- 1 g ( x ) = lim x 2 + g ( x ) = lim x 0 g ( x ) = lim x 2 g ( x ) = 6
Additional Properties Thm – If f ( x ) g ( x ) for all x near a (except possibly at a ) and lim x a f ( x ) and lim x a g ( x ) exist then

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