January 4, 2006 9:40 am
Larson section 1.2

Cost = 0.75  -  0.50 (-Floor[-(t - 1)])

p1 = Plot[Cost, {t, 0, 5}, PlotStyle -> Red];

t = List[3,  3.3, 3.4, 3.6,  3.7,  4, 5]

cost35 = 0.75  -  0.50 (-Floor[-(t - 1)])

t2 = List[2, 2.5, 2.9, 3, 3.1, 3.5, 4]

cost35 = 0.75  -  0.50 (-Floor[-(t2 - 1)])

The limit of cost35 as t approaches 3 does not exist as the function approaches -.25 from below and -.75 from above.

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

Plot[y, {x, 1, 3}, PlotStyle -> Red];

y

Clear y

y

Remove [y]

y

y = x^2

Remove[x]

y

I am lost. I cannot seem to get rid of the x and y and start over.

Remove[x, y]

x

y

y = x^2

Limit[y, x -> 2]

Now I seem to have it working.

Remove[x, y]

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

Limit[y, x -> 2]

try1 = List[1.9, 1.99, 1.999, 2.001, 2.01, 2.1]

y1 = List[y, try1]

2:35 PM I want to try working with equations and tables and lists again...

2 + 2

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

x = List[1.9, 1.99, 1.999, 2.001, 2.01, 2.1]

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

The limit appears to be 0.333...

Limit[y, x -> 2]

Clear [y, x]

y

x

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

Limit[y, x -> 2]

The difficulty is primarily with making sure that everything has been cleared.

Clear[x, y]

y = (x - 2)/(x^2 - 4)

Limit[y, x -> 2]

Plot[y, {x, 1, 3}, PlotStyle -> Red];

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

Clear[y, x]

y = (Sqrt[x + 3] - Sqrt[3])/x

Limit[y, x -> 0]

Clear[y, x]

y = ((Sqrt[x + 5]) - 3)/(x - 4)

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

Limit[y, x -> 4]

Clear[y, x]

y = (x - 9)/(Sqrt[x] - 3)

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

Limit[y, x -> 9]

Clear[y, x]

y = (x - 3)/(x^2 - 9)

Limit[y, x -> 3]

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

3:05 PM This has been a satisfying 30 minutes.