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# calc final - âˆ 1 5 3 1 cot x dt t t dx d XI(10 points Find...

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Math211 – Final December 13, 2005 Name:________________________

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III. (10 pts ) Use the limit definition to prove x x f 6 ) ( ' = for 5 3 ) ( 2 - = x x f . IV. (10 pt) Find the equation of the tangent line for 5 3 2 2 = + - y xy x at ) 1 , 2 ( . = y ________________
V. (5pts each) Differentiate each of the following functions. 1. x x x y sin 2 2 + + = 2. x y x cos 2 = 3. ) sec( x e y = 4. 1 2 - = x x y

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VII. (5 points each) Find each of the general indefinite integrals. 1. = + + - + - dx x x x x 1 2 3 7 4 6 2 3 2. = dx x ) sin( π 3. = - dx x x 2 1 8
VIII. (5 points each) Find the exact value for each of the followings: 1. = + + + - + - - xdx x x x x x x x cos tan 2 sin 2 4 6 8 2 5 4 / 4 / 7 π π 2. - - - - 0 3 2 9 1 2 dx x x IX. (5 points) Use the Fundamental Theorem of Calculus-I to simplify the followings:

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Unformatted text preview: + âˆ« 1 5 3 1 cot x dt t t dx d XI (10 points) Find the point on the line 2 3 = + y x that is closet to the point (2, 2). XII (10 pts) A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 10 ft higher than the bow of the boat. In order to make the boat approaching the dock in a rate of 5ft/min when it is 24 ft from the dock, how fast the rope should be pulled from the pulley?...
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calc final - âˆ 1 5 3 1 cot x dt t t dx d XI(10 points Find...

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