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Unformatted text preview: x . lim x 1 x 1 x 2 6 x + 5 = lim x 1 x 1 ( x 1)( x 5) = lim x 1 1 x 5 = 1 1 5 = 1 4 . Question 4 2 We consider the function f ( x ) = b if x Q x 2 if x n Q a ) Is the function f continuous at x = 0 ? Answer : Yes Justify your answer in one line. For x Q , f ( x ) = 0 0 = f (0) as x 0. For x n Q , f ( x ) = x 2 0 = f (0) as x b ) Does the derivative of f exist at x = 0 ? Answer : Yes and f (0) = 0 Justify your answer in one line. For x Q , f ( x ) = 0 and f ( x ) f (0) x = 0 0 as x 0. For x n Q , f ( x ) = x 2 and f ( x ) f (0) x = x 2 x = x 0 as x 0. . Note : Try to visualize the graph of f in your mind. Is it a nice continuous curve ?...
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This note was uploaded on 04/08/2010 for the course MATH MAT1330 taught by Professor Rad during the Spring '10 term at University of Ottawa.
 Spring '10
 Rad
 Calculus

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