Tutorial2(0211)

# Tutorial2(0211) - x = 2 5 Consider the function f x = x | x...

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T2/MATH0211/2009-10 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH0211 Basic Applicable Mathematics Tutorial 2 1. Show that a linear function f ( x ) = mx + c , where m 6 = 0 , is injective. Find the inverse of it and show that it is also a linear function. 2. Evaluate lim x 0 - x 2 - 3 x + 2 x 3 - 2 x 2 and lim x 2 - x 2 - 3 x + 2 x 3 - 2 x 2 . 3. Find the value of A so that the function f ( x ) = 3 - 9 + x 2 x if x 6 = 0 , A if x = 0 is continuous at x = 0 . 4. Let f ( x ) = x 2 if 2 < x 4 , x if 0 x 2 (a) Is f ( x ) continuous at x = 2 ? (b) Is f ( x ) left-continuous and right-continuous at
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Unformatted text preview: x = 2 ? 5. Consider the function f ( x ) = x- | x | x for x ∈ [-1 , 0) ∪ (0 , 1] . Can f ( x ) be deﬁned at x = 0 so that it will be continuous there? Discussion I. Correct to three decimal places, what is the value of the smallest positive root of the equation 18 x 3-27 x 2-2 x + 3 = 0 ? II. Is the bisection method applicable to discontinuous functions? 1...
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