1007_Tut1 - x + y ) . H int: U s e t h e g ive n in fo r m...

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M AT H 1007 A T utor ial #1 Sept 22, 2006 Fir st N ame: Last N ame: Student N o: N o Calculator s! E xample of a pr oof: To s h o w t h a t 2 c s c 2 x = s e c x c s c x , we s t a r t wit h o n e s id e , s a y t h e le ft s id e ( L S ) , a n d s h o w t h a t it is e qu a l t o t h e o t h e r s id e : L S = 2 c s c 2 x = 2 s in 2 x = 2 2 s in x c o s x = 1 s in x c o s x = p 1 s in x Pp 1 c o s x P = c s c x s e c x = R S 1. [2 mar ks] P r o ve t h e fo llo win g t r ig o n o m e t r ic id e n t it y, u s in g t h e a p p r o a c h a b o ve . ( s in x + c o s x ) 2 = 1 + s in 2 x 2. [2 mar ks] Fin d t h e s lo p e a n d t h e e qu a t io n o f t h e t a n g e n t lin e t o t h e c u r ve y = x 3 a t t h e p o in t wh e r e x = 1 . 1
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3. [4 mar ks] If s in x = 12 13 a n d s e c y = 5 4 , wh e r e x y lie b e t we e n 0 a n d π 2 , c a lc u lu t e s in (
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Unformatted text preview: x + y ) . H int: U s e t h e g ive n in fo r m a t io n t o b u ild 2 r ig h t t r ia n g le s , o n e wit h a n g le x a n d o n e wit h a n g le y . Y o u kn o w 2 o f t h e 3 s id e s o f t h e t r ia n g le b y u s in g t h e S OH -CA H -TOA r u le . N o w u s e t h e p yt h a g o r e a n t h e o r e m t o s o lve fo r t h e 3 r d s id e o f t h e t r ia n g le . 4. [2 mar ks] U s in g t h e defnition o f c o n t in u it y ( ie , u s in g lim it s ) , s h o w t h a t f ( x ) = x 2 − x − 2 x − 2 if x n = 2 1 if x = 2 is N OT c o n t in u o u s a t x = 2 . 2...
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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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1007_Tut1 - x + y ) . H int: U s e t h e g ive n in fo r m...

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