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Unformatted text preview: 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 ; 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 = / 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 Rolles Theorem....
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- Spring '08