S06 1205 final W - Name ID MATH 1205 CRN FINAL Spring...

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Name: MATH 1205 FINAL Spring, 2006 ID #: CRN: (50 pts total) Free Response Questions Read the Directions. CALCULATORS MAY BE USED You must SHOW ALL WORK and use methods learned in class to receive full credit. 1. (8 pts) Use optimization techniques to determine what is the largest possible area for a right triangle whose hypotenuse is 5 cm long? 2. (6 pts) Use the graph to find the following. If the limit does not exist, give a reason . a) lim x !" 1 f ( x ) = b) lim x " 3 f ( x ) = c) Name the x values where f ( x ) is discontinuous
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3. (8 pts) A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 2 ft s , how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 ft from the wall? 4. (12 pts) Find dy dx of each of the following functions. Simplify your answers. a) y = e 2 x ( ) ( x 2 + 1) (Use Quotient Rule) b) y = sin(3ln x ) c) 3 x 2 y 4 = y
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5. (7 pts) Evaluate the following limits. State
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