MATH 1351 TI-85 EXERCISE IV

Graphical investigations of limiting behavior

Name: SID:

1. Graph each of the following in the ZDECM viewing window. Explain the presence of the discontinuity at x = 1 and discuss the limiting behavior as x approaches 1.

a. y = (x^2 - 1) / (x - 1)

b. y = | x^2 - 1 | / (x - 1)

c. y = (x^2 - 1) / |x - 1|

2. In problem #1 write each function in terms of equations of lines on various intervals. (Problems 41 - 43 on page 20 are examples of such.)

a	b..	c.

y =	y =	y =

3. a. Estimate the limit to 5 decimal places as x goes to 0 of the expression	(1 + x )^(1/x) .

b. Compute e^1.

4. Graph the function y = (sin x ) / x in RADIAN MODE . Using TRACE and ZOOM estimate the limit as x approaches 0.

5. a. Repeat exercise #4 in DEGREE MODE. The limit to 5 decimal places is approximately

b. Recall that 1 degree equals Pi/180 radian . Compute Pi/180 .

6. Return to RADIAN MODE, sketch the graph and "evaluate" the limiting behavior as x approaches 0 for each of the following functions.

a. y = sin ( 1 / x )

b. y = x sin ( 1 / x)

c. y = x^2 sin ( 1 / x )

In your own words describe the difference you observe between the graphs of a, b and c. (It might help to "overlay" the graphs of y = 1 & y = -1 on the graph of a, the graphs of y = x &

y = -x on the graph of b, and the graphs of y = x^2 and y = - x^2 on the graph of c.)