Math 1A - Fall 2004 - Borcherds - Midterm 2

Math 1A - Fall 2004 - Borcherds - Midterm 2 - (a:72 20 on...

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Math 1A Midterm 2 2OO4-17-3 2:OO-3:3Opm. You are allowed I sheet of notes. Calculators are not allowed. Each question is worth 1 mark, which will be given only for a clea.r correct answeland conect working. There is no partial credit for wtong answers. 1. Difierentiate g = o/cos(g). 2. Differentiate y = tan(cos(r)). 3. Find d.y ld.a by implicit difierentiation if a2y2 + xsin(y) = 4. 4. Firrd the 43rddcrivative of sin(2"r). to .\s' 5, Use logarithmic difierentiation (o! any other method you know) to find the deri tive of thc function g : r'. 6. Fird the derivative of sinh(or). 7. Use differentials or a linear approximation to estimate 2.0013. 8. Find the absolute maximum and absolute minimum values of
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Unformatted text preview: !(a) :72 - 20 on the interral [0,3]. O a,", all critical numbers of the function /(z) = c l1(s). Show thdt the equatiol 2 + 4a + 2ax * 5c5 = 0 has exactly one real root. Find the intervals on which / is increasing or decrcasing and all local maximum irnd rninimum values of f(x) = aa' . Find the limit lim.-o o2/ cos(c). Find thc limit lirn,--6(sin(r) - e)/e3. In questiors l4 and l5 your skctch should show the maxima and minima. where the function i slrow corrvexirl or poj4ls o,l inflecliol. 14. Skctch the curve I = x 3:11/3. 15. Sketch tLe curve y : (x - I)/x2. 10. 1 1 . 12. 13....
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