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1432finalexamreview - Math 1432 Final Exam Review 1 Give...

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Math 1432 Final Exam Review 1. Give the equation of the tangent line to the given graph at the point where x = 0 a. x e x x f 2 ) 1 6 ln( ) ( + + = b. x e x x f 4 3 ) 1 2 ln( ) ( - - + = c. 2 9 ) ( x x f - = 2. Give an equation relating x and y for the curve given parametrically by a. ( ) 1 3tan ( ) 1 2sec x t t y t t = - + = + b. 2 ( ) 2 ( ) 1 3 t t x t e y t e - = = - 3. Differentiate the function: a. 2 ( ) x f x e = b. ( ( ) tan ln f x x = c. sin ( ) x f x x = d. ( ) sinh(3 ) f x x = e. cosh ( ) x f x x = 4. Integrate: a. ( + dx x x ) 2 sinh( ) 3 cosh( b. 3 x e dx c. ( 3 ln x dx x d. ( 7 sinh(5 ) x e x dx - e. + dx x x ) 3 ( cos 16 ) 3 sin( 2 f. + dx x x 4 4 6 g. dx x ) 3 tan( h. + dx x x 2 9 1 ) 3 arctan( i. + dx x 2 4 1
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j. dx x - 2 9 k. dx x ) 4 ln( 3 l. dx e x x 2 m. - + dx x x x ) 4 )( 1 ( 14 5 2 n. + + + + dx x x x x ) 1 )( 1 ( 2 5 2 2 o. - dx x x 2 2 9 2 p. dx x ) 10 arctan( 2 q. dx x x ) 2 cos( 3 5. Determine if the following sequences converge or diverge. If they converge, give the limit. a. 2 1 n n + b.
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