M408Cprac3 - (ln x ). 6. Find y if y = (1 + x 2 ) tan x ....

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M408C Sample Test 3, sec’s 4.9–7.6 No Calculators, books, notes, etc. 1. Evaluate Z 3 x 2 + 1 3 x + sec 2 x dx . 2. Evaluate Z π/ 4 0 sin 5 x cos x dx. 3. R is the region in the plane bounded by y = x , y = 0 and x = 4. Find the volume of the solid formed by rotating R about the line y = - 1. 4. Evaluate Z 2 0 x x + 2 dx. 5. Find y 0 if y = 3 e sin x + sec( e x ) + sec - 1
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Unformatted text preview: (ln x ). 6. Find y if y = (1 + x 2 ) tan x . 7. Show that d dx (arctan x ) = 1 1 + x 2 . 8. Find the intervals over which f ( x ) = ln x/ x is concave up. 9. Use the limit denition of denite integral to evaluate Z 5 2 3 x 2-4 x + 5 dx ....
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This note was uploaded on 05/02/2011 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas at Austin.

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