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Review for Test 1 (1.5 - 2.3)

# Review for Test 1 (1.5 - 2.3) - MAC2233 Review for Test...

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MAC2233 9/1/10 Review for Test 1 (1.5 – 2.3) Section 1.5 Find the ( 29 2 lim x f x →- if it exists: 1. ___________________ 2. ___________________ Find the indicated limit, if it exists; or show that it does not exist: 3. x x x 9 3 lim 9 - - ___________________ 4. ( 29 ( 29 2 2 1 1 1 2 lim x x x →- + - ______________ 5. x x x x 2 7 2 3 lim 7 →- + - + _________________ 6. Find x x x x 5 5 3 5 7 lim 3 4 2 →±∞ - + + ___________________ 7. Suppose the time for a rat to traverse a maze on the n th trial was approximately ( 29 5 17 n T n n + = minutes. What happens to the time of traverse as the number of trials n increases? In other words, find 5 17 lim n n n →∞ + . ___________________ Section 1.6 Find the ( 29 0 lim x f x - →- and ( 29 0 lim x f x - →- 8. ( 29 0 lim x f x - = ____ ; ( 29 0 lim x f x + = ____ 9. ( 29 0 lim x f x - = ____ ; ( 29 0 lim x f x + = ____

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MAC2233 9/1/10 10. Find the ( 29 6 lim x f x - →- and ( 29 6 lim x f x + →- if ( 29 3 2 4 6 x f x x - - = - ____________________________ 11. Find the ( 29 0 lim x f x - and ( 29 0 lim x f x + if ( 29 - + = - - x , x f x x , x 2 1 1 0 3 1 1 0 4 . Is the function continuous? ( 29 ( 29 0 0 lim _____ lim _____ x x f x f x + - = = ____________________________ 12. Find the ( 29 5 lim x f x - and ( 29 5 lim x f x + if ( 29 - = - x f x x 3 5 . Is the function continuous? 13. List all values of x for which ( 29 2 2 8 16 6 x x f x x x - + = - - is not continuous. 14. Is f(x) = -7x 6 – 8x 3 + x 2 – 12 continuous at x = 738? Explain or who why or why not? _________________ Section 2.1 14. a. Find and simplify the difference quotient for the function  f(x) = -2x 2  + 7x + 8 b. Find the slope of the tangent line at x = -3. ________________ c. Find the average rate of change with respect to x as f(x) changes from x = -2 to x = 4 . 15. A manufacturer can produce CD players at a cost of \$50 each. It is estimated that if the players are sold for p dollars each, consumers with buy q = 250 - p recorders each month. At what rate is profit changing when q = 75. Is profits increasing or decreasing at this level of production?
MAC2233 9/1/10 Section 2.2 16. Differentiate ( 29 8 7 9 10 6 4 7 5 16 08 7 35 8 . . x f x x x x = + + - + 17. Find the equation of the line that is tangent to the graph of f(x) = 5x 3 – 4x 2 + 3 at x = -2. 18. It is estimated that t years from now, the population of a certain town will be p(t) = t 2 + 500t + 62,500. Express the percentage rate of change of the population as a function of t and simplify algebraically.

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Review for Test 1 (1.5 - 2.3) - MAC2233 Review for Test...

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