March 23, 2006 11:10 am
Larson ch 1.4, p. 75 - 78.
2.

y = 1/(x - 2)

p1 = Plot[y, {x, -5, 5}, PlotStyle -> Blue];

Clear[y, p1]

y = (x^2 + 2  x)/(x + 2)

p1 = Plot[y, {x, -5, 5}, PlotStyle -> Red];

Clear[y, p1]

y = (1/(x - 2)) + (x^2 + 2  x)/(x + 2)

p1 = Plot[y, {x, -10, 5}, PlotStyle -> Green];

Now to try some one-sided limits.
11.

Limit[(x - 5)/(x^2 - 25), x -> 5, 
      Direction -> -1]

12.

Limit[(2 - x)/(x^2 - 4), x -> 2,  
      Direction -> -1]

13.

y = x/Sqrt[x^2 - 4]

Limit[y, x -> 2, Direction -> -1]

Limit[y, x -> 2, Direction -> 1]

-I ∞

I am not sure what this symbolism means!

Plot[y, {x, -10, 5}, PlotStyle -> Red];