MATH 125g Midterm: fall2005_short
4 Aug 2020
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December 2005: (6 points each) calculate the following limits, lim x 4, lim x 1, lim x 0 x 4. 3x + x2 sin x: (7 points each) find dy dx, y = ln(2x2 3x). 2x 3: y = ex+1 , y = xsin x (use logarithmic di erentiation), y = z tan x. 0: (8 points each) evaluate the following integrals: 1 (a) z 2 x2(x 2) (b) z sin x dx. 2x(x2 12) (x2 + 4)3: (5 points) find the in ection points of f and determine where f is concave upwards and downwards, (8 points) draw a rough sketch of the graph of f . If the material used to make the top and bottom is twice as expensive as the material used to make the side, nd the dimensions of the least expensive can. 8. (17 points) a tank in the shape of an inverted circular cone is standing on its tip.
