CK-12-Calculus

http://www.ck12.org Chapter 1. Functions, Limits, and Continuity

Multimedia Links

For a presentation of continuity using limits(2.0), see Math Video Tutorials by James Sousa, Continuity Using Li
mits (5:44).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/530

For a video presentation of the Intermediate Value Theorem(3.0), see Just Math Tutoring, Intermediate Value Theor
em (7:53).

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/531

Review Questions

1. Generate the graph off(x) = (|x+ 1 |)/(x+ 1 )using your calculator and discuss the continuity of the function.


2. Generate the graph off(x) = ( 3 x− 6 )/(x^2 − 4 )using your calculator and discuss the continuity of the function.

Compute the limits in #3 - 6.

3. limx→ 0 +

√x

√

1 +√x− 1

4. limx→ 2 −|x−x 23 |−(x^8 − 2 )


5. limx→ 1 +^2 xx|x−− 11 |


6. limx→− 2 −||xx++^22 |−|+xx+−^22

In problems 7 and 8, explain how you know that the function has a root in the given interval. (Hint: Use the
Intermediate Value Function to show that there is at least one zero of the function in the indicated interval.):

7. f(x) =x^3 + 2 x^2 −x+1, in the interval(− 2 ,− 3 )


8. f(x) =√x−√^3 x−1, in the interval( 9 , 10 )


9. State whether the indicatedx−values correspond to maximum or minimum values of the function depicted
   below.