Math 1431 – Fall 2017 EMCF 2 – Covers 1.5, 2.1 and 2.2 Due Thursday, 9/21 at 11:59pm Instructions • Submit this assignment at http://www.casa.uh.edu under "EMCF" and choose EMCF 2. 1. If f (2) = 3 and f ’ (2) = –1, find an equation of the tangent line when x = 2. a. y – 3 = 2(x + 1) b. y – 2 = 3(x + 1) c. y + 1 = 2(x – 2) d. y – 3 = –1(x – 2) e. none of the above 2. If f (x) = 2xx−+, which of the following will calculate the derivative of f (x)? a. ( ) ( )lim→−++−−+22h0xxh xxh b. ()( )lim→−++−−+22x0xxh xxh c. lim→x0 ( ) ( )( )− + + + −− +22xh xh x xh d. ( ) ( )( )lim→− + + + −− +22h0xh xh x xh e. none of these 3. Let ( )23fx x x= −. Give the value of ( ) ( )011limhf hfh→+−. a. 1 b. -1 c. -2 d. DNE e. 2 f. None of these.4. Give the slope of the tangent line to the graph of ( )22fx x x= − at the point where x = 1. a. 2 b. 0 c. 1 d. DNE e. -1 f. None of these. 5. Differentiability implies continuity. a. True b. False 6. Continuity implies differentiability. a. True b. False 7. Give a value of A so that the function ( )22,2,2xx xfxx Ax x−<=−≥ is continuous. a. 1 b. 0 c. There is no such value. d. 2 e. 3 f. None of these. 8. The Intermediate Value Theorem can be used to show that there is a solution to on [–2, 4]. a. True b. False 9. Let ( )121fxx=+. Give the value of ( ) ( )hfhfh11lim0−+→. a. 2/9 b. -2/9 c. -1/3 d. DNE e. 1/3 f. None of these.10. Give the smallest value of x for which the derivative of 3() 3 2fx x x=−+ is 0. a. -1 b. 1 c. -2 d. 2 e. 0 f. None of
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