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Day41-1432class - Math 1432 REVIEW The one posted plus some...

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Math 1432 REVIEW The one posted plus some extra problems that were included in previous semesters, noted with a (*). FINAL EXAM Dec 13 – 15 CASA Register as soon as possible on Dec. 6. Double (triple?) check your date and time. Have someone call you the day of the exam!
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1. Give the equation of the tangent line to the given graph at the point where x = 0 a. ( 29 ( 29 2x x 6x 1 e f ln = + + b. ( 29 ( 29 4x x 2x 1 3e f ln - = + - c. ( 29 2 x 9 x f = -
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2. Find the inverse of the following, if possible: a. ( 29 2 x 3 x f = - b. ( 29 x 1 x x 2 f + = +
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3. Find the derivative of the inverse for the following: a. ( 29 ( 29 ( 29 ( 29 3 1 x x 1 2 9 9 f , f , f ' - = + = = b. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 3 1 1 2 3 3 1 2 1 f , f , f ' , f ' , f ' - - = = - = = - = c. ( 29 x f passes through the points ( 3 , –2 ) and ( –2 , 1 ). The slope of the tangent line to the graph of ( 29 x f at x = 3 is –1/4. Evaluate the derivative of the inverse of f at –2.
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4. Find the equation of the tangent and the normal lines to the parametric curves at the given points: a. ( 29 ( 29 ( 29 x t 2 2t y t 4 2t 2 4 cos , , , = - = + - b. ( 29 ( 29 ( 29 ( 29 x t 3 3t 2t y t 1 5t 3 1 cos , , , = + = +
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5. Give an equation relating x and y for the curve given parametrically by a. ( 29 ( 29 x t 1 3 t y t 1 2 t cos sin = - + = + b. ( 29 ( 29 x t 1 3 t y t 1 2 t cosh sinh = - + = + c. ( 29 ( 29 t t x t 1 4e y t 2 3e - = - + = +
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6. Differentiate the function: a. 2 ( ) 3 x f x = b. ( 29 ( 29 5 f x tan log x = c. sin ( ) x f x x = d. ( ) sinh(3 ) f x x = e. cosh ( ) x f x x =
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7. Integrate: a. ( 29 3x 2x dx cosh( ) sinh( ) + b. 3x 4 dx c. ( 29 3 2 x dx x log d. ( 29 7 x 2 5x dx sinh( ) -
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e. 2 3x dx 16 3x sin( ) cos ( ) + f. 4 6x dx 4 x + g. ( 29 3x dx tan h. 2 3x dx 1 9x arctan( ) +
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i. 2 1 dx 4 x + j. 2 9 x dx - k. ( 29 3 4x dx ln
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l. 2 x x e dx m. ( 29 ( 29 2 5x 14 dx x 1 x 4 + + - n. ( 29 ( 29 2 2 x 5x 2 dx x 1 x 1 + + + +
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o. 2 2 2x dx 9 x - p. ( 29 2 10x dx arctan q. ( 29 3x 2x dx cos
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8. Write an expression for the nth term of the sequence: a. 1, 4, 7, 10, … b. 2, –1, 1 1 1 2 4 8 , , , .... - 9. Determine if the following sequences are monotonic. Also indicate if the sequence is bounded and if it is give the least upper bound and/or greatest lower bound.
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