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Calc 1 WA 5 - WA 5 Calculus I Chapter 5 Section 5.1 dr d 6...

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WA 5 Calculus I Chapter 5 Section 5.1 6) dr d r d d π θ πθ π θ = = = 10) 2 2 1 1 1 1 dx x x dx x c c x - - + - + - 12) 2 3 4 2 ( 3) 3 3 4 2 x x dx x dx x x c + + = + + 32) ( 29 2 3 2 2 ( sin ) cos 3 ... 3 ' sin sin 3 t t dt t t c check t d t t t - = + + = + - = -
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38) 2 2 sec (tan sec ) (tan )(sec ) sec sec tan ... ' (tan )(sec ) sec sec (tan sec ) y y y dy y y y dy y y c check d y y y y y y - - = - + = - = - 54) 2 2 2 2 2 2 2 2 2(3 ) 2 2(3) 1 2 2 1 dy x dx x y x c c c y x x = - (3,2 29 = - + = - + - = - = - - 56) 3 0 ( ,3) 1 3 3ln 3 ln 3 3ln 3 dy x e dx x dy x dx y x c e c c y e = = + = + - = = + Should be 3ln│x│+C 70) 1 1 1 2 2 2 2 ''( ) sin '( ) sin cos '(0) cos0 1 2 ( ) cos 2 sin 2 (0) 6 sin(0) 2(0) 6 6 0 0 6 f x x f x x dx x c f c c f x x x x c f c c c = = = - + = - + = - = = - + = + + = = + + = = + + - =
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74) 10 0 10 1/2 0 10 1/2 0 3/2 1 3/2 1 1 3/2 100 1 so100 ( ) 100 2 100( ) 3 2(0) 500 100( ) 3 500 @ 7 2(7) 100( ) 500 3 1,734.68 dp k t where k K dt k t dt k t dt t dt t P c c c day P P = = = = + = + = = + = 80) 2 0 2 0 0 2 2 2 2 2 ( ) 32 / sec ( ) 32 (1/ 2) ( ) 0 (1/ 2)( 32 ) (8 )( ) 64 sec sec 0 16( )( ) 8 ( ) 64 sec sec 2.2655sec ( ) 32( )(2.2655sec) 8 sec 64.496 sec f a t ft v t t v s at v t s ft ft t t ft ft ft t t ft t ft v t ft = - = - + = + + = - + + = + + = = - + = - Section 5.2 2) 6 3 ( 2) 3(3 2) 4(4 2) 5(5 2) 6(6 2) 3 8 15 24 50 k k k = - = - + - + - + - = + + + =
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10) 2 2 4 2 1 1 4 1 ( ) .... 1 ( ) 4 4 1 ( ) 4 x x = - + - - V 16) ( 29 15 1 15 15 1 1 2 3 2 3 15(15 1) 2( ) (15(3)) 2 2(120) 45 240 45 195 I i i i i = = = - = - = + - = - = - = � � Section 5.3 6) 3 2 1 3 (3 1) 2 0 x dx x n n x as x - = = = - - V V 28) ( 29 8 0 8 0 2 2 2 2 (8 ) 8, 8 1 ( ) 2 1 (8)(8) 32 2 (8 ) 32 1 1 (8 ) (8 ) 2 2 1 1 (8)(8 8 ) (8)(0) ( )(0 ) 2 2 64 32 0 32 x dx h b triangle A bh A A x dx x x x x - = = = = = = - = = - - - = - - - = - - =
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44) a) 0 1 0 1 1 1 ( ) ( ) ( ( ) ) 0 ( 5) 5 f x dx
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