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test2practice

# test2practice - MATH 151 SPRING 2006 COMMON EXAM II VERSION...

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PART I 1. (4 pts) If g ( x ) = ( x 3 + x ) 5 , then g 0 ( - 1) = (a) 320 (b) 160 (c) 80 (d) 40 (e) 0 2. (4 pts) 4 ln 2 + ln 3 4 = (a) ln 12 (b) ln 6 (c) ln 25 (d) ln 54 (e) ln 24 Exam continues on next page 2
3. (4 pts) Find the slope of the tangent line to the curve sin( xy ) = x 2 - 3 at the point 3 , π 3 . (a) - 2 (b) - 2 - 3 π (c) - 2 + 3 2 π (d) - 2 - π 3 (e) - 2 + π 3 4. (4 pts) If f ( x ) = 1 x + 2 , then the inverse function of f ( x ) is Exam continues on next page 3

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5. (4 pts) lim t 0 sin 2 (4 t ) 2 t 2 = 6. (4 pts) If f ( x ) = x + sin( x ) + 2 e 3 x and g ( x ) = f - 1 ( x ) , then g 0 (2) = Exam continues on next page 4
7. (4 pts) If h ( x ) = sin 2 (3 x ) , then h 00 ( x ) = (a) 6 cos(3 x ) (b) 18(cos 2 (3 x ) - sin 2 (3 x )) (c) 18 (d) 9(cos 2 (3 x ) - 1) (e) 9 sin 2 (3 x ) 8. (4 pts) Find the linear approximation of f ( x ) = 1 x at a = 4 . Exam continues on next page 5

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9. (4 pts) The length of leg AB of right triangle ABC increases at a rate of 2 inches per second and the length of leg BC increases at a rate of 6 inches per second. At what rate in inches per second does the hypotenuse increase when AB = 3 and BC = 4 ? 10. (4 pts) lim x →-∞ 2 - e 5 x 1 + e 2 x = Exam continues on next page 6
11. (4 pts) A curve C is given by the parametric equations x = 2 t 3 - 3 t 2 , y = t 2 - t . Find all horizontal and vertical tangents. (a) horizontal tangent at t = 0 and t = 1 , vertical tangent at t = 1 2 . (b) horizontal tangent at t = 1 2 , vertical tangent at t = 0 and t = 1 . (c) horizontal tangent at t = - 1 and t = 1 , vertical tangent at t = 2 . (d) horizontal tangent at t = 2 , vertical tangent at t = - 1 and t = 1 . (e) None of the above

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