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

In[1]:=

y = 1/(x - 2)

Out[1]=

1/(-2 + x)

In[5]:=

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

[Graphics:HTMLFiles/index_4.gif]

In[11]:=

Clear[y, p1]

In[15]:=

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

Out[15]=

(2 x + x^2)/(2 + x)

In[16]:=

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

[Graphics:HTMLFiles/index_9.gif]

In[17]:=

Clear[y, p1]

In[18]:=

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

Out[18]=

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

In[20]:=

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

[Graphics:HTMLFiles/index_14.gif]

Now to try some one-sided limits.
11.

In[21]:=

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

Out[21]=

1/10

12.

In[22]:=

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

Out[22]=

-1/4

13.

In[23]:=

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

Out[23]=

x/(-4 + x^2)^(1/2)

In[24]:=

Limit[y, x2, Direction -1]

Out[24]=

∞

In[25]:=

Limit[y, x2, Direction1]

Out[25]=

- ∞

- ∞

I am not sure what this symbolism means!

In[26]:=

Plot[y, {x, -10, 5}, PlotStyleRed] ;

Plot :: plnr : y is not a machine-size real number at x = -1.9124902107820516`. More…

Plot :: plnr : y is not a machine-size real number at x = -1.9859155293368975`. More…

Plot :: plnr : y is not a machine-size real number at x = -1.9941185827017225`. More…

General :: stop : Further output of Plot :: plnr will be suppressed during this calculation. More…

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