10.03 - [Discuss True-False problems on page 70.] 1....

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[Discuss True-False problems on page 70.] 1. “If f is a function, then f ( s + t ) = f ( s ) + f ( t ).” ..?. . False. Example: f ( x ) = x 2 , s = t = 1. Note however that it IS true that ( f + g )( t ) = f ( t ) + g ( t ); that’s the definition of f + g . 2. “If f ( s ) = f ( t ), then s = t .” ..?. . False. Example: f ( x ) = x 2 , s = –1, t = 1. Note however that the converse is true: if s = t then f ( s ) = f ( t ). 3. “A vertical line intersects the graph of a function at most once.” ..?. . True. This is the vertical line test. 4. “If f and g are functions, then f ° g = g ° f .” ..?. . False. Example: f ( x ) = x +1, g ( x ) = x 2 . Or: f ( x ) = x +1, g ( x ) = 2 x . Or: f ( x ) = 2, g ( x ) = 3 for all x .
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5. “lim x 4 ((2 x )/( x –4) – 8/( x –4)) = lim x 4 (2 x )/( x –4) – lim x 4 8/( x –4).” ..?. . False. The two limits on the right hand side do not exist, so Limit Law 2 does not apply. (In fact, the limit on the left hand side equals 2.) 6. “lim
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This note was uploaded on 02/13/2012 for the course MATH 141 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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10.03 - [Discuss True-False problems on page 70.] 1....

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