{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

solutions_09_18

# solutions_09_18 - Math 1a Continuity(Solutions 1 At which...

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

Math 1a: Continuity (Solutions) September 18, 2009 1. At which values of x are the following functions continuous? 1. a ( x ) = b x c , the greatest integer less than or equal to x . For all x except the integers: . . . , - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 , . . . . 2. b ( x ) = the taxi fare (in dollars) for distance x (in miles). Assume that the meter ticks every 0 . 1 miles. Note that the function is defined only for x > 0. It is continuous for all x > 0 except x = 0 . 1 , 0 . 2 , 0 . 3 , . . . . 3. c ( x ) = sin( x ) + cos( x ) . Continuous for all x . 4. d ( x ) = | x | , the absolute value of x . Continuous for all 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? Solution. No, it is not. The price function is discontinuous at time t = 1 min , 2 min , 3 min , . . . . 3. Define the function f ( x ) by f ( x ) = xe cos(1 /x ) for x 6 = 0 . How should I define f (0) to make f continuous? Solution. For the function to be continuous, f (0) should be defined so that f (0) = lim x 0 f ( x ) .

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.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern