21f08-ex2-review-solutions-1

21f08-ex2-review-solutions-1 - AFA8EEFEXA# h e a e ia ha ib...

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Unformatted text preview: AFA8EEFEXA# h e a e ia ha ib e e ed h iea i f e i4 h eha i e e i45 ek e h ig i i e e fh k da id jh eh ighed if h ik aha e fda iak e a fh ee i Y h d ka h ee i a fe ha e iedha d eh e b e ih k iga h ebk h e e fh e h e b igged i d ig h eea ig ig ha e hd a h a k ig h e b e f ka h e i e e ih k ig h gh h ed e a ih e i eeh e e hd ed i h e i h ih i ak eha b e ea ie eb i h e ea h k h e b e F id h e f igd e ia i e a d dx ( x sin x ) . i : F i dea ih hee e i ie fA a heee e i ih b h heba ead hee e f i fh dbe e ed i e e ia ihba e e : x sin( x ) = parenleftBig e ln( x ) parenrightBig sin( x ) = e (ln( x ) sin( x )) . hed iee ia e : d dx ( x sin x ) = d dx parenleftBig e (ln( x ) sin( x )) parenrightBig = e (ln( x ) sin( x )) parenleftbigg d dx (ln( x ) sin( x )) parenrightbigg = e (ln( x ) sin( x )) parenleftbigg 1 x sin( x ) + ln( x ) cos( x ) parenrightbigg . Y d i if iab ib h d b (ln(tan( x ) + sec( x ))) . i : h iha adda e : (ln(tan x + sec x )) = (tan x + sec x ) (tan x + sec x ) = sec 2 ( x ) + sec( x ) tan( x ) (tan x + sec x ) = (tan x + sec x ) sec( x ) (tan x + sec x ) = sec( x ) . e e b e h i e ; e i eed if i eg a i (cosh(2 x + 3)) . AFA8EEFEXA# i : igh eha i ead h ed e ia i e f cosh( x ) (cosh(2 x + 3)) = sinh(2 x + 3)2 = 2 sinh(2 x + 3) . d d dx ( sin 1 ( x 2 ) ) . i :: ( sin 1 ( x 2 ) ) = 1 radicalbig 1- ( x 2 ) 2 (2 x ) = 2 x 1- x 4 . e ( x 2 ln( x ) ) = i : a ih h e d e h i e ( x 2 ln( x ) ) = 2 x ln( x ) + x 2 1 x = 2 x ln( x ) + x....
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This note was uploaded on 11/06/2009 for the course MATH 21 taught by Professor Stanley during the Spring '09 term at Lehigh University .

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21f08-ex2-review-solutions-1 - AFA8EEFEXA# h e a e ia ha ib...

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