Sheet (8) solution - Math 103 Class Work Sheet (8) Solution...

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1 Math 103 Class Work Sheet (8) Solution [1] (i) c x x x dx x x dx x x 16 ln 16 2 16 16 4 4 2 2 2 (ii) c x dx x dx x ) 1 5 cos( 5 1 5 ) 1 5 sin( 5 1 ) 1 5 sin( (iii) c x dx x dx x ) 6 sinh( 6 1 6 ) 6 cosh( 6 1 ) 6 cosh( (iv) c x dx x dx x ) 5 6 tan( 6 1 6 ) 5 6 ( sec 6 1 ) 5 6 ( sec 2 2 (v) c dx dx dx x x x x x x ) 150 ln( 150 150 25 6 5 6 2 (vi) c x dx x dx x ) 5 4 ln( 4 1 5 4 4 4 1 5 4 1 (vii) c x dx x dx x 6 ) 7 2 ( 2 1 2 ) 7 2 ( 2 1 ) 7 2 ( 6 7 7 (viii) c x c x dx x dx x 2 3 2 3 ) 5 2 ( 3 1 2 3 ) 5 2 ( 2 1 2 5 2 2 1 5 2 (ix) c e dx e dx e dx e x x x x 6 16 6 16 6 16 ) 3 8 ( 2 6 1 6 6 1 (x) c x h dx x x dx x x dx x x 2 csc 2 1 2 1 2 1 2 1 2 1 2 1 2 1 4 1 1 2 2 2 (xi) c x dx x dx x dx x 14 sin 14 1 14 1 1 14 1 14 1 14 1 1 2 2 2 (xii) c x h dx x x h dx x x h ) 1 3 ( csc 3 1 3 ) 1 3 coth( ) 1 3 ( csc 3 1 ) 1 3 coth( ) 1 3 ( csc [2] (a) 3 12 ) ( ' x x f c x dx x x f 4 3 3 12 ) ( the point ) 8 , 1 ( lies on the curve 11 3 8 c c 11 3 ) ( 4 x x f 232 11 ) 3 ( 3 ) 3 ( 4 f
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2 (b) t t a 6 2 ) ( 5 ) 0 ( v 4 ) 0 ( s 1 2 3 2 ) 6 2 ( ) ( ) ( c t t dt t dt t a t v 5 3 2 ) ( 5 5 ) 0 ( 2 1  t t t v c v 2 3 2 2 5 ) 5 3 2 ( ) ( ) ( c t t t dt t t dt t v t s 4 5 ) ( 4 4 ) 0 ( 3 2 2  t t t t s c s (c) Car starts from rest 0 ) 0 ( v Constant acceleration c t a ) ( It travels 500 ft in 10 sec 0 ) 0 ( s 500 ) 10 ( s 1 ) ( ) ( c ct dt c dt t a t v ct t v c v  ) ( 0 0 ) 0 ( 1 2 2 2 ) ( ) ( c ct dt ct dt t v t s 2 ) ( 0 0 ) 0 ( 2 2 ct t s c s  2 2 5 ) ( 10 2 ) 10 ( 500 500 ) 10 ( t t s c c s  2 sec / 10 ) ( feet t a [3] (i) c x dx x x dx x x 11 ) 3 2 ( 2 1 ) 2 ( ) 3 2 ( 2 1 ) 3 2 ( 11 2 10 2 10 2 (ii) c x dx x x dx x x 3 4 ) 7 3 ( 9 1 ) 9 ( 7 3 9 1 7 3 3 4 3 2
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This note was uploaded on 01/09/2010 for the course MATH Math103 taught by Professor Dr.prof.mostafaamer during the Spring '09 term at German University in Cairo.

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Sheet (8) solution - Math 103 Class Work Sheet (8) Solution...

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