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Math 408C Quiz _3 '07

# Math 408C Quiz _3 '07 - g(x = e sin(x then g(x = e cos(x 15...

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Math 408C Name_______________________________ Quiz #3 Fall 2006 True-False (3 pts each) _______ 1. The domain of f(x) = arccos(x) is [0, π ]. _______ 2. e 2ln(3) = 9 . _______ 3. If y = xarctan(x), then dy dx = x 1+ x 2 . _______ 4. ln(x 2 e - 2x ) = 2[ln(x) - x] _______ 5. As x tends to ( , the slope of the tangent line to y = arctan(x) tends to 0. _______ 6. sec(x)tan(x)dx = tan 2 (x) 2 + C _______ 7. darcsin(x) dx + darccos(x) dx = 0 _______ 8. If G(x) = cos(t 2 x 1 )dt , then ( G (x) = - cos(x 2 ) . _______ 9. If ln(3x – 1) = ln(17) , the x = 6. _______ 10. If f is the inverse of g and both have derivatives, then ( g (x) = 1 f (g(x)) _______ 11. If h(x) = 7 x , then ( h (x) = x7 x- 1 . _______ 12. The tangent to the curve x 2 e y + ye x = 0 at (0,0) has slope 1. _______ 13. 3x 2 e x 3 dx = e x 3 + C _______ 14. If

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Unformatted text preview: g(x) = e sin(x) , then ( g (x) = e cos(x) _______ 15. x 2 (4 + x 3 ) 5 dx = (4 + x 3 ) 6 18 + C . _______ 16. The maximum value of arcos(x) occurs when x = -1. _______ 17. cos(arctan( 3 4 ) = 4 5 _______ 18. (x +1) (x- 1) = e (x+1)ln(x- 1) . _______ 19. x lim-arctan(x) = -p 2 20. (8 pts) How did we define ln(x)? What area has value ln(2)? Use this to give an estimate of ln(2). How would you use the previous to estimate ln(1024)? (Hint: 1024 = 2 10 ) 21. (15 pts) The area enclosed between the curves y = x and y = x 2 is rotated around the x-axis. Find the resulting volume. 22. (10 pts each) Find the indicated integrals. e x 5 + e x dx cos(3x) 1+ sin 2 (3x) dx 5 2x 1 dx...
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