exercise_problems(0211)solution

exercise_problems(0211)solution - , 5] ∩ Z 1 5. (a) key:...

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SE1Sol/MATH0211/2009-10 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH0211 Basic Applicable Mathematics Sketched Solutions to Supplementary Exercise 1 1. Let A = [ - 2 , 3) ,B = { x R : | 3 x - 2 | ≤ 4 } C = (1 , 4) Z Find the following sets (1) C can also be written as { 2 , 3 } , so R \ C = R \ { 2 , 3 } = ( -∞ , 2) (2 , 3) (3 , ) . (2) B = ( -∞ , - 3 / 2] [1 / 2 , ) . Therefore, A B = [ - 2 , - 3 2 ] [ 1 2 , 3) , A B = R . (3) B \ A = ( -∞ , - 2) [3 , ) (4) 2. (i) (a) 3 (b) 189 (ii) 3 and 36 3. See graphs in another file. (a) domain ( -∞ , - 5] [ 5 , ) range [0 , ) (b) domain R \{- 3 } range R \{ 1 } (c) domain R \{ 4 , - 1 } range R (d) domain ( - 3 , 3) range [1 / 3 , ) (e) domain R range [ - 1 , 1) (h) domain [0 , 2) range [0 , ) 4. (a) natural domain R range [0 , 1) (b) See another file (c) lim x 1 - f ( x ) = 1 , lim x 1 + f ( x ) = 0 , and lim x 1 f ( x ) does not exist. (d) No, f is discontinuous at every point in [0
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Unformatted text preview: , 5] ∩ Z 1 5. (a) key: x-√ x 2-1 = 1 x + √ x 2-1 (b) key: √ x + 3-√ 3 x = 1 √ x + 3 + √ 3 6. Evaluate the following limits: (a)-2423 784 (b) (c) 3 x 2 (d) 1 5 (e) (f) ∞ (g) ∞ 7. From the graph (another file) we could observe that all the functions are continuous in (0 , 1) , and (a) left-continuous at 1 , and right-continuous at (b) left-continuous at 1 , but not right-continuous at (c) left-continuous at 1 , and right-continuous at (d) left-continuous at 1 , but not right-continuous at (e) not left-continuous at 1 , and right-continuous at 2...
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exercise_problems(0211)solution - , 5] ∩ Z 1 5. (a) key:...

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