{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

handout_09_18

# handout_09_18 - f x by f x = xe cos(1/x for x 6 = 0 How...

This preview shows pages 1–2. Sign up to view the full content.

Math 1a: Continuity September 18, 2009 1. At which values of x are the following functions continuous? (a) a ( x ) = b x c , the greatest integer less than or equal to x . (b) b ( x ) = the taxi fare (in dollars) for distance x (in miles). Assume that the meter ticks every 0 . 1 miles. (c) c ( x ) = sin( x ) + cos( x ) . (d) d ( x ) = | x | , the absolute value of x . 2. A phone plan states that “Charges are calculated on a per minute basis, and rounded up to the next whole minute”. Is the price of a phone call a continuous function of its length?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f ( x ) by f ( x ) = xe cos(1 /x ) for x 6 = 0 . How should I deﬁne f (0) to make f continuous? 4. Deﬁne the function f ( x ) by f ( x ) = cos( x ) if x < 0, ax + b if 0 ≤ x ≤ 2, x 3 if 2 < x . What should the constants a and b be so that f ( x ) is continuous for all x ? 5. (Challenge problem) Deﬁne f ( x ) by f ( x ) = ( 1 if x is rational, if x is irrational. At which points is f ( x ) continuous? 2...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

handout_09_18 - f x by f x = xe cos(1/x for x 6 = 0 How...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online