Exam 2 Practice 1 - a MATH 1 27 M IDTERM l 1 7 N ovember2...

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a MATH 127 MIDTERM #l 17 November 2005 SPECIAL CoDE: 111705 p.2 of 5 .1. Calculate the derivative f (x) for f(x) : e-'*/(xt) a) -2(x+ 1) e-2*/(x) b) -2(x - 1) e-2*/1xt; c) -2(x + 1) e-2*/(x2) d) -2(x - 1) e-2*l1xt1 e) -2 e-2* tl1x31 .2. Which of the equations given below best approximates the equation of the tangent line to the graph of y: x In(x) at the point (x:2, y:2ln(2)): a) y-2 :1.386(x-.693) b) y- 1.386:1.693(x-2) c) y-1.386 :2(x-1.386) d) y -.693 : 1.386(x-.693) e) y - 2.386:1.693(x -2) .3. If f(x): ln(x2) then the SECOND derivative f'(x) is: a) Ux? b) 2lx2 c) 2tx d) -21x2 e) _21x3 .4. If y = f(x) : 1x2 + l;1/2, then f (x) is: a) (tt2)(x2 * l)t't b) (2x)(x2 + t)t't c) (2x)(x2 + l)t'' d) x(x2 + l)-ltz e) x1x2 + lyr/2 .5. If f(x) : (e'^ - x;rt2 , then f (x) is: a) (zez' - 1)ttz b) (U2)(e2' - x)-t/z c) (ll2)(e2* - xyt/212e2* - x1 d) (ll2)(e2* - xyrt212e2* - l'1 e) -U2 ("'* - * yt/212e2* - l'1 .6. The cost of producing q units of a certainproduct is givenby C(q) : 1000 + 30 ekq where k is a positive constant. At a production level of 30 units, the cost of producing an additional unit is about: a) 30 b) 30e30k c) 30ke30k d) 30kee e) 1000+30e30k .7. Suppose f(x) = yrt.^ Then f(x) is which of the following: a) l/e* b) (1 + xex)/e^ c) (1 - xe^/e* d) (l - x)/e* e) (l + x)/e. PDF Creator - PDF4Free v2.0 http://www. pdf4free. com
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MATH 127 MIDTERM #1 17 November2005 SPECIAL CODE: 111705 p.3 of 5 .8. Find the equation of the tangent line to the graph of y: e'+ xe-t* at x: -1.
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