# UK MA 123 - Chapter 5: Practice/review problems (6 pages)

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## Chapter 5: Practice/review problems

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Lecture Notes

- Pages:
- 6
- School:
- University of Kentucky
- Course:
- Ma 123 - Elem Calc & Its Applics

**Unformatted text preview: **

Formulas for derivatives Chapter 5 Practice review problems The collection of problems listed below contains questions taken from previous MA123 exams Derivatives 1 If f x 6x2 3x 1 find f x a 6x 1 b 12x 3 c 12x 1 d 2x 3 e 2x 5 2 If f x x3 4x2 2x 1 then f x a 3x2 8x 3 x2 x 1 b d 3x2 8x 1 c 3x2 8x 2 e 3x2 4x 1 3 If f x x3 then f 1 h f 1 h 0 h Hint Relate the limit to the derivative of f x lim a 0 b 1 c 2 d 3 e 4 4 Suppose f t t3 t2 t 1 Find the limit f 1 h f 1 h 0 h lim Hint Relate the limit to the derivative a 1 b 0 c 1 d 2 e The limit does not exist 5 If Q s s7 1 find Q 1 h Q 1 h 0 h lim a 2 6 If f x x 1 a 3 b 5 find b 3 c 6 d 7 e 8 d 1 e Does not exist f 1 h f 1 h 0 h lim c 1 7 Let f x x x x Find the derivative f 0 by evaluating the limit f h f 0 h 0 h lim a 2 b 1 c 0 d 1 61 e Does not exist 8 Let x denote the greatest integer function Recall the definition x equals the greatest integer less than or equal to x How many points are there in the interval 1 2 9 2 where the derivative of x is not defined a 1 b 2 c 3 d 4 e 5 The product rule 9 Suppose that h x f x g x Assume that f 2 3 f 2 2 g 2 1 and g 2 5 Find h 2 a 20 b 17 c 11 d 13 e Cannot be determined d 16 e 32 10 If h t t 1 t 1 t2 1 then h 2 equals a 0 b 4 c 8 11 Let k x x 3 x 4 x 1 Find k x a 12 b 3x2 16x 19 d 3x2 14x 16 c 3x2 18x 20 e 1 12 If R x x 2 x2 2 x3 2 find R 2 a 0 b 12 c 48 d 8 e 6 The quotient rule 13 If f x a x2 x 1 then f x x 1 2 1 b 14 Suppose that f x a 8 a c 2 x 1 2 d 2 1 x2 e 2 x 1 2 x2 1 Find f 3 x 4 b 15 Find Y s if Y s 2 x 1 2 9 c 10 d 14 e 16 1 5 2 4s s 5 3 s s 2 2 b d 1 s 3 5s 2

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