Math1314Test2Review

# Math1314Test2Review - lim x x f b → 2 lim x x f c 2 lim...

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Math 1314 Test 2 Review 1 Math 1314 Test 2 Review In numbers 1 – 7, find the limit. 1. 3 2 2 lim 2 3 1 + - + - - x x x x 2. 1 lim 3 1 - + x x x x 3. 1 lim 3 1 - - x x x x 4. Given the following graph of a function f , find 4 ) ( lim x x f if it exists.

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Math 1314 Test 2 Review 2 Limits at Infinity: If the degree of the numerator is smaller than the degree of the denominator, then . 0 ) ( ) ( lim = x g x f x If the degree of the numerator is the same as the degree of the denominator, then you can find ) ( ) ( lim x g x f x by making a fraction from the leading coefficients of the numerator and denominator and then reducing to lowest terms. If the degree of the numerator is larger than the degree of the denominator, then it’s best to work the problem by dividing each term by the highest power of x in the denominator and simplifying. You can then decide if the function approaches or - , depending on the relative powers and the coefficients. 5. 3 2 1 2 2 lim x x x x - + - - 6. 1 6 5 2 lim + - x x x 7. x x x x + - + + - 1 1 lim 2 3 8. Find the following limits given: - < = 5 5 2 1 2 ) ( 2 x x x and x x x x x f a. - 2 ) (

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Unformatted text preview: lim x x f b. + → 2 ) ( lim x x f c. 2 ) ( lim → x x f Math 1314 Test 2 Review 3 9. Where is 8 2 4 ) ( 2---= x x x x f continuous? 10. Use the four step process to find the derivative of x x x f 3 2 ) ( 2 + = . 11. Find the average rate of change of 1 3 . 02 . ) ( 2 + +-= x x x f over [5,15]. Math 1314 Test 2 Review 4 For numbers 12 – 21, find the first derivative. 12. 1 2 5 3 1 ) ( 2 3---= x x x x f 13. ( 29 x x x f 2 ln ) ( 2 = 14. 1 2 ) ( 2-= x x x f 15. 1 2 ) ( 2 3 +-= x x x f Math 1314 Test 2 Review 5 16. 1 2 2 ) (--= x e x f 17. 5 2 ) 3 2 ln( ) ( + = x x f 18. [ ] ) 1 )( 3 5 ( ln ) (-+ = x x x f 19. --= 1 2 4 ln ) ( x x x f 20. 3 ) 2 4 ( 3 ) (-= x x x f Math 1314 Test 2 Review 6 21. 5 ) ( 2-= x x f For numbers 22 – 25, find the second derivative. 22. x e x x f 2 3 4 ) (-= 23. 4 3 ) 1 ( ) (-= x x f 24. x xe x f 4 6 ) ( = Math 1314 Test 2 Review 7 25. 4 ) 2 ( 1 ) ( + = x x f...
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Math1314Test2Review - lim x x f b → 2 lim x x f c 2 lim...

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