Sheet (3) Solution

# Sheet (3) Solution - Math 103 Class Work Sheet(3...

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1 Math 103 Class Work Sheet (3) Solution [1] (i)   59 1 ) 2 ( ) 2 ( 2 ) 2 ( 3 1 2 3 lim 2 4 2 4 2 x x x x (ii) 12 9 4 ) 2 ( 6 ) 2 ( 1 ) 2 ( 2 4 6 1 2 lim 2 2 2 2 2 x x x x (iii)     4 6 ) 2 ( 3 ) 2 ( 6 3 lim 6 3 lim 4 4 2 4 2 x x x x x x (iv) 0 0 2 6 lim 2 2 x x x x 5 ) 3 ( lim 2 ) 2 )( 3 ( lim 2 2 x x x x x x (v) 0 0 3 7 2 9 lim 2 2 3 t t t t 5 6 5 6 ) 3 )( 1 2 ( ) 3 )( 3 ( lim 3 t t t t t (vi) 0 0 8 ) 2 ( lim 3 0 h h h          4 ) 2 ( 2 2 4 ) 2 ( 2 2 ) 2 ( ) 2 ( ) 2 ( ) 2 ( 8 ) 2 ( 2 2 3 3 3 h h h h h h h h         12 4 ) 2 ( 2 2 lim 4 ) 2 ( 2 2 lim 8 ) 2 ( lim 2 0 2 0 3 0 h h h h h h h h h h h Or using rule   m n m m n n a x a m n a x a x lim Let 2 h x 12 ) 2 ( 1 3 2 2 lim 8 ) 2 ( lim 1 3 3 3 2 3 0 x x h h x h (vii) 0 0 3 9 lim 9 t t t   6 3 lim ) 3 ( ) 3 )( 3 ( lim 3 9 lim 9 9 9 t t t t t t t t t (viii) 0 0 3 81 lim 2 9 x x x     108 6 * 18 ) 9 )( 3 ( lim 3 ) 9 )( 3 )( 3 ( lim 3 ) 9 )( 9 ( lim 3 81 lim 9 9 9 2 9 x x x x x x x x x x x x x x x

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2 (ix) t t t t 1 1 1 lim 0 0 0 1 1 1 lim 0 t t t t     2 1 1 1 1 1 1 1 1 ) 1 ( lim 1 1 1 1 . 1 1 1 lim 0 0 t t t t t t t t t t t (x) 0 0 1 lim 2 1 x x x x Let x y      3 3 * 1 1 1 1 lim . lim 1 1 lim 1 lim 1 lim 2 1 1 3 1 4 1 2 1 y y y y y y y y y y y x x x y y y y x (xi) 2 1 2 1 lim 2 2 ) 2 ( 2 2 2 lim 2 | 2 | lim 2 2
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Sheet (3) Solution - Math 103 Class Work Sheet(3...

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