# ws06 - WORKSHEET 6 Fall 1995 1 A function is said to be...

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WORKSHEET 6 - Fall 1995 1. A function is said to be continuous at a point x 0 if i. f ( x 0 ) is deFned; ii. lim x x 0 f ( x ) exists; iii. and lim x x 0 f ( x )= f ( x 0 ) . Determine whether the following functions are continuous at the points given. At discontinuous points, indicate which of the conditions above do not hold. a) x 0 = 2 , 1b ) x 0 = 3 , 1c ) x 0 = 1 , 0 , 2 1 -2 -3 1 -1 2 0 d) f ( x x 2 +5 ,x < 1; 6 x, x = 1; 27 x +33 ,x> 1. at x 0 = 1e ) f ( x ± θ sin 1 θ 6 =0; 0 =0. at x 0 =0 2. Given below is a one-parameter family of functions . That is, it is a collection of many functions { f t } - one for each value of the parameter t . Determine which values of this parameter give a continuous function. f t ( x ± t sin x, x π 2 ; t 2 x 2 > π 2 . 3. a) State the Squeeze Theorem. b) Use part a) to Fnd lim x c f ( x )g iventhat ² ² ² ² f ( x ) f ( c ) x c ² ² ² ² M for x 6 = c. 4. Suppose that lim x c D ( x L. a) Why is the following statement impossible?

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## This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.

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ws06 - WORKSHEET 6 Fall 1995 1 A function is said to be...

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