# wksht5 - ESP Kouba Worksheet5 1 Differentiate each of the...

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Unformatted text preview: ESP Kouba Worksheet5 1. Differentiate each of the following. X a. F(x)=arcsin(ex2) b. F(x)=ln{1+_[\}t3+5dt} o 3 c. Fix) = m d. F(x) =l cosx2. 63in? x2 dx ln(tanx) 0 Sinx ‘lx-l e. F(x)=le1-tdt r. F(x)=lcos(t2+1)dt 1 3 3 x3 g. F(x)=l cos(t2+1)dt h. F(x)=l(3-t5)100dt X-l i x x i. F(x) =x5-l t2 dt 0 t2+1 2. Find the x-value(s) for which each of the following functions has a global minimum value. a. F(x) = ex2'7 X b. F(x) = 9 +1 (t-1)(2—t)6 dt for x_>_0 o 3. Evaluate the following definite integrals. Think carefully. Nothing sophisticated is needed to solve these problems. .9. o a. l(2/x2 + x2/2)dx b. l(1+x)2 dx l ~l 1r ° I C- I (1+X)200 dx Cl. I smx dX ‘l 0 coszx 1r 3 i e. I (sinx+cosx)2dx f. l x2(1+x3)1/1° dx 1 0 4 w 5%, g. I coszx dx h. I 5e025xdx o o 1 if: i. I2xsec2(x2)dx j. I (xcosx+sinx)dx o o 4. a. Make a sketch of the region bounded by the graphs of y = 1/2 x , y = 2 , and x = 0 . b. Set up definite integrals which represent the volumes of the solids formed by revolving the region in part a. around i. the x-axis ii. the y—axis 5. A large bucket full of water weighing 100 lbs. is slowly lowered 25 feet by a rope and pulley. a. How much work is done in lowering the bucket ? b. How much work is done in lowering the bucket if the bucket is leaking , losing 4 in.3 of water per foot lowered. (Assume that one cubic foot of water weighs 62.4 lbs.) 6. Find the average value of each function over the indicated interval. a. f(x) = x 3 on [0, 1] b. f(x)=sinx on [0,1t/2] c. f(x)=2xex2 on [xlln2', \lins'] d. f(x) = x sec 2 x + tan x on [0, 1/2] ...
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