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Be able to find the domain of a composition exercises

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Be able to find the domain of a composition Exercises: In the following, identify the domains of f , g , g f , and f g : 1. f ( x ) = x 2 - 1 and g ( x ) = 1 /x 2. f ( x ) = x and g ( x ) = x 2 3. f ( x ) = x 3 - 6 x 2 + 11 x - 6 and g ( x ) = x 4. f ( x ) = 6 x 2 +10 x +24 and g ( x ) = x - 2 5. f ( x ) = ( x + 3) - 1 / 2 and g ( x ) = x 2 - 4
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Limits: Calculate one and two sided limits especially by applying Theorem 1 Handling indeterminate forms Rationalizing numerator/denominator to take a limit Calculate limits at infinity When in doubt, draw a graph! Exercises: Find the following limits. 1. lim x →- 1 7 x 2 - 2 x + 5 2. lim x 1 x 3 - 1 x - 1 3. lim x 3 x 2 + 2 x - 15 x - 3 4. lim x 0 | x | x 5. lim x 2 x 2 - 1 x < 2 5 x = 2 5 - x x > 2 6. lim x →- 1 ( | x | x ≤ - 1 3 x + 2 x > - 1 7. lim x 9 x - 3 x - 9 8. lim x →∞ 3 x 4 - 15 x 2 + 7 x 92 x 3 + 17 x 2 - 35 x + 1 9. lim x →-∞ 19 x 7 + 12 x 6 - 23 x 4 + 2 x - 108 2 x 7 - 106 x 6 + 14 x 5 + 14 x 2 10. lim x →∞ - 4 x 3 + 2 x 2 - x + 4 3 x 4 + x 3 - 7 x 2 + 1
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Continuity: Intuitive and graphical notions of continuity Limit definition of continuity Properties of continuous functions (the list that is derived from Theorem 1) When is a rational function continuous Applying the Intermediate Value Theorem Taking limits of continuous functions Exercises: 1. Identify where the following functions are continuous: i.
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