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Unformatted text preview:  , say so. (5 pts each): a. lim x 1 x 23 x + 2 + ( x1) cos( x1) x1 = b. lim x 2 + 3 x 2 x 2x2 = c. lim x 3 x 2 x 2x2 = 3. Where is g ( x ) = x 21 x < cos x2 0 x < 3 + sin x x discontinuous? Justify your answer. 4. There are two points on the curve y = x 2 where the tangent line passes through (2 , 3). Find both. (16 pts). 5. Suppose lim x f ( x ) = 1, lim x g ( x ) = 0, lim x 1 f ( x ) = 2 and lim x 1 g ( x ) = 3. Find (3 points each): lim x ( g f )( x ) = lim x 1 ( f + g )( x1) = lim x (( gf ) f )( x ) = lim x 1 ( ( f ( x )) 2 + 1 ) = 6. Find lim x 1 x 2x + 1cos( x1) x1 . (12 pts). 7. According to the denition of the derivative, if f ( x ) = 1 x1 then f ( x ) can be expressed as a limit. Write out this limit expression (3 pts) and evaluate (9 pts). 8. Find lim x x cos 1 x . Justify carefully. (12 pts)....
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This note was uploaded on 07/17/2008 for the course MATH 151 taught by Professor Any during the Summer '08 term at Ohio State.
 Summer '08
 Any
 Math, Calculus

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