1001_1.5_Lab_3

1001_1.5_Lab_3 - find the values of x where f(x) is...

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CALCULUS 1 LAB 3 NAME: ___________________PARTNER: _________________ 1.5 Continuous Functions GSA: ______________________Lab Time: ___________ Definition: f is continuous at c x = if all of the following conditions are true: (i) f(c) exists, c " D f , (c,f(c)) is on the graph, (ii) ) ( lim x f c x ! exists and (iii) lim x " c f ( x ) = f ( c ) . Theorem: If the functions f and g are continuous at c then (a) f ( x ) ± g ( x ) is continuous at c, (b) f ( x ) g ( x ) is continuous at c, (c) f ( x ) / g ( x ) is continuous at c if g ( c ) " 0 and has a discontinuity at c if g ( c ) = 0 . 1. a) Give the three conditions that are necessary for the function f(x) to be continuous at c x = . (i) (ii) (iii) b) From the graph of f(x)(see board),
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Unformatted text preview: find the values of x where f(x) is discontinuous and state all conditions in part (a) that fail to hold. 2. Given f ( x ) = kx 2 , x " 2 2 x + k , x > 2 # $ % . Find a value for the constant k that will make the function f(x) continuous everywhere: 3. Find the values of x at which f(x) is discontinuous. Use interval notation (if possible) to describe the set of values where f(x) is continuous. (a) f ( x ) = e x x " 2 , (b) f ( x ) = x ln( x ) , (c) f ( x ) = cot( x ) = cos( x ) sin( x ) , (d) f ( x ) = x " 3 x 2 " 2 x " 3 , (e) f ( x ) = x 4 " 3 x 2 + 8...
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