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fin09pmk - MAC 2311 Final Exam and Key PM Prof S Hudson...

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MAC 2311 PM April 20, 2009 Final Exam and Key Prof. S. Hudson 1) (20 pts) Compute and simplify; R e 2 x dx = R sec( x )(sec( x ) + tan( x )) dx = R 1 1+16 t 2 dt = R t 1+16 t 2 dt = 2) (10 pts) Suppose a particle has velocity v ( t ) = 3 t + 2 at time t . Suppose it begins at position s (0) = 5. Find its position after 3 seconds. 3) (15 pts) Compute y 0 ; a) y = (2 x ) x b) y = log 3 (2 x ) c) y = sin - 1 ( x + 1) 4) (10 pts) Find the slope of the tangent line to the curve, x = sec( t ), y = tan( t ) at the point where t = π/ 3. For maximum credit, use the chain rule as done in class. 5) (10 pts) Assume oil spilled from a ruptured tanker spreads in a circular pattern whose radius increases at a constant rate of 2ft/s. How fast is the area of the spill increasing when the radius of the spill is 60ft ? 6) (10 pts) CHOOSE ONE (you may continue on the back or on extra paper); A) State and prove Rolle’s Theorem. B) State and prove the Product Rule. 7) (10 pts) Answer TRUE or FALSE: 1

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f ( x ) = ln | x | is an increasing function. A continuous function defined on ( -∞ , + ) must have a minimum value. A rational function is continuous except where the denominator is zero. If f is differentiable on the open interval ( a, b ) then it is continuous on
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