Review 1-solutions-1 - white (taw933) Review 1 ben-zvi...

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white (taw933) – Review 1 – ben-zvi – (55600) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Below is the graph oF a Function f . 2 4 6 2 4 6 2 4 2 4 Use this graph to determine all oF the values oF x on ( 7 , 7) at which f is discontinuous. 1. none oF the other answers 2. no values oF x 3. x = 1 , 1 correct 4. x = 1 5. x = 1 Explanation: Since f ( x ) is defned everywhere on ( 7 , 7), the Function f will be discontinuous at a point x 0 in ( 7 , 7) iF and only iF lim x x 0 f ( x ) n = f ( x 0 ) or iF lim x x 0 f ( x ) n = lim x x 0 + f ( x ) . As the graph shows, the only possible candi- dates For x 0 are x 0 = 1 and x 0 = 1. But at x 0 = 1, f (1) = 4 n = lim x 1 f ( x ) = 0 , while at x 0 = 1, lim x →− 1 f ( x ) = 4 n = lim x →− 1+ f ( x ) = 0 . Consequently, on ( 7 , 7) the Function f is discontinuous only at x = 1 , 1 . 002 10.0 points ±ind all values oF x at which the Function f defned by f ( x ) = x 7 x 2 5 is not continuous? 1. x = 5 2. x = 7 3. x = 7 , 5 , 5 4. no values oF x 5. x = 5 6. x = 5 , 5 correct Explanation: Because f is a rational Function it will Fail to be continuous only at zeros oF the denomi- nator, i.e. , at the solutions oF x 2 = 5 . Consequently, f Fails to be continuous only at x = 5 , 5 . 003 10.0 points Below is the graph oF a Function f . 2 4 6 2 4 6 2 4 6 8 2 4
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white (taw933) – Review 1 – ben-zvi – (55600) 2 Use the graph to determine all the values of x in ( 6 , 6) at which f is not diFerentiable. 1. x = 3 2. x = 3 , 2 3. x = 1 , 2 4. x = 3 , 1 , 2 correct 5. x = 3 , 1 Explanation: The graph shows that f has a removable discontinuity at x = 3 and a jump disconti- inuity at x = 2, so f will not be diFerentiable at these points. On the other hand, at x = 1 the graph is continuous but has a ‘corner’, so it will not be diFerentiable at this point also. Thus, on ( 6 , 6) the function f will fail to be diFerentiable at the points x = 3 , 1 , 2 . 004 10.0 points After t seconds the displacement, s ( t ), of a particle moving rightwards along the t -axis is given (in feet) by s ( t ) = 1 2 t 3 . ±ind the average velocity of the particle over the time interval [1 , 1 + h ]. 1.
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Review 1-solutions-1 - white (taw933) Review 1 ben-zvi...

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