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1205ctf_f01 - 1 If f(x =(e2x 1,then f(1 = 1 8 e2 1 7 8 2 16...

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1. If f ( x ) = ( e 2 x + 1) 8 ,then f 0 (1) = 1) 8 ( e 2 + 1 ) 7 2) 16 ( e 2 + 1 ) 7 3) 8 e 2 ( e 2 + 1 ) 7 4) 16 e 2 ( e 2 + 1 ) 7 2. Which of the following functions has a removable discontinuity at x = 0? 1) x sin 1 x 2) ln( x ) 3) x - 1 4) x - 1 x 2 - 1 3. The following picture shows the graphs of f , f 0 , and f 00 . Identify each curve. 1 2 3 4 x -4 -2 2 4 y a:regular , b:dashed , c:thick 1) f = a f 0 = b f 00 = c 2) f = c f 0 = b f 00 = a 3) f = a f 0 = c f 00 = b 4) f = b f 0 = c f 00 = a 4. Consider the function f ( x ) = x 3 - 6 x on the interval [ - 2 , 2]. Which of the following statements is true? 1) The absolute maximum value of f is 4. 2) The absolute maximum value of f is 4 2. 3) The absolute maximum value of f is 5. 4) There is no absolute maximum value of f on the interval. 5. Suppose z = x 3 y 2 where both x and y are changing with time. At a certain instant when x = 1 and y = 2, x is decreasing at the rate of 2 units/sec and y is increasing at the rate of 3 units/sec. How fast is z changing at this instant and is it increasing or decreasing?
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