MATH 1007 Review

MATH 1007 Review - MATH 1007 Review Problems December 2005...

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Unformatted text preview: MATH 1007 Review Problems December 2005 Page 1 Prepared by S . Alaca, A.A. J arai and A.B. Mingarelli 1. Find lim x sin x x x 2 . 2. Find lim x ln( x + 1) x x 2 . 3. Find lim x xe x . 4. What is lim x + x 2 ln x ? 5. If 0 2 and cos = 3 2 , what is sin ? 6. Solve the equation cos 2 = 3 2 for 0 2 ? 7. If 0 2 and tan = 3, what are sin and cos ? 8. What is the equation of the tangent line to the curve x 3 + y 3 = 6 xy at the point (3 , 3)? 9. At what points is the tangent to the curve y = x 2 e x horizontal? 10. What is the equation of the tangent line to the curve y = x ln x at the point (1 /e 2 , 2 /e 2 )? 11. Let f ( t ) = ln t t 3 . What is f (2)? 12. Let h ( x ) = x 2 cos x . What is the value of h ( / 2)? 13. Let f ( x ) = x 3 x x 2 + x . What is f (1)? 14. Let f ( t ) = sin t 1 + cos t . What is f ( / 3)? MATH 1007 Review Problems December 2005 Page 2 15. Let g ( x ) = x 2 ln x . What is the value of g (1 /e )? 16. Let u ( t ) = e t cos t . What is the value of u (1)? 17. Let f ( x ) = sin 1 ( x 2 ). What is f ( x )? 18. Let f ( x ) = arctan(2 x + 1). What is f (1 / 2)? 19. Let f ( x ) = arcsin(2 x + 1). Find the equation of the tangent line to y = f ( x ) at ( 1 / 2 , 0)....
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This note was uploaded on 03/22/2010 for the course MATH 1007 taught by Professor Unknown during the Fall '07 term at Carleton.

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MATH 1007 Review - MATH 1007 Review Problems December 2005...

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