Sinx sin 1 2 sinx2 s sinx sinx 1 inx2 sinx2

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Unformatted text preview: ityfandatx)e= x)e,cos()x+ e f (x)2 esin(x) Local = 00 (x) = x sin( +sin(x ) cos( x 22 (x) = Pointsx)eInfection (find2f’’(x))) sin( of sin(x) + cos(x) esin(x x) f 0 (x) = cos(x)esin(sin(x) f 00 (x) = 00 (sin(=) esin(x))2cos(in(2 )D in(x) 2 R} 00 2 ) x s = {x f)e x) x cos(x x)s xsin(x) f (x) = sin(x e ⇡+⇡ 3 cos( 3⇡ e , cos(x) = 0 x) > x = 2 , = 00 sin( 2 f ( x) = e cos(x)2 2 in(x) s (2k + f 00⇡x) = 00 =) cos(x)2 = sin(x) 1) ( f )0(x) k =) cos(x)2 = 00 , where= 0is2an integer = sin(x) 2 f (x) = esin(x cos(x) 2 sin(x) 2 sin ( 1) cos(x) cos(x) x= sin(x) = sin( ) 1 2 sin(x)2 s= sin(x= sin(x) 1 in(x)2 ) sin(x)2 sin(x)2x+ sin(=)0 1 = 0 + sin( ) 1 x p p p p 4( (5) 1 1 ± 1 2 412 1)(1) 1)(1) 1± ( (5) 1 ± sin(x)sin(x) = = = ±= 2 2 2 2 22 sin(x) = sin(x) + sin(x) 1 = 0 1 p p 1 ± 12 4( 1)(1) (5) 1 =)± x f 002x) = 0 =) cos(x22 = sin(2 ) sin(x ( p p)2 = sin(x) 1± 1 cos(x (5) x = arcsin 1 ±sin(x)2 = sin(x) = ⇡sin(x) 2 2 sin(x) = sin(x)2 + sin(x) 1 = 0 p p 2 = 1± 1 0 1 4( 1)(1) = 1 ± x(5) , 2 2 10 2 p 0 arcsin 1 ± (5) ⇡ x= 2 2 0 3 10 , 10 0 Plotting the Curve p (5) 1 rcsinL’hopitals Rule: ± ⇡ 2 2 Case 1 10 , 10 0 0 Action Use L’hopital’s rule. (Take derivative of top and bottom) sin(x) cos(x) f (x) = lim = lim =1 x!0 x!0 x 1 3 x = lim x!0 sin(1) x lim =1 cos(x) = lim =1 x!0 1 x L Case’hopital’sction A Rule cos(x) lim = 1 Move one of the x!0 1 to the 0 · 1 functions 0 · 1 bottom so we can use L’hopital’s rule 0·1 x!0 lim+ x ln(x) = lim+ x!0 1 ( ) = lim+ 1 x! 0 x!0 1 x 1 x2 ln(x) 1 x 1 ( ) = lim+ 1 x! 0 = lim+ x = 0 x!0 1 x 1 x2 = lim+ x!0 (x) 1 x 1 1 ( 1 + x!0x x2lim ) = lim 1 = x ! 0+ x2 x ! 0+ L Case’hopital’s Rule Action Pull out a common factor 11 1 0 1 0 1 0 ,1 ,1 x ! 0+ x=0 1 1 L Case’hopital’s Rule A...
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