March 09, 2006 5:30 am
Larson ch 1.3, p. 64 - 66
39.

In[1]:=

y = (x^3 + 8)/(x + 2)

Out[1]=

(8 + x^3)/(2 + x)

In[2]:=

Limit[y, x -2]

Out[2]=

12

In[3]:=

Plot[y, {x, -5, 5}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_6.gif]

40.

In[4]:=

Clear[y]

In[5]:=

y = (x^3 + 1)/(x + 1)

Out[5]=

(1 + x^3)/(1 + x)

In[6]:=

Limit[y, x -1]

Out[6]=

3

In[7]:=

Plot[y, {x, -5, 5}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_13.gif]

41.

In[8]:=

Clear[y]

In[9]:=

y = (x - 5)/(x^2 - 25)

Out[9]=

(-5 + x)/(-25 + x^2)

In[10]:=

Limit[y, x5]

Out[10]=

1/10

In[11]:=

Plot[y, {x, -5, 5}, PlotStyle Red] ;

[Graphics:HTMLFiles/index_20.gif]

42.

In[12]:=

Clear[y]

In[13]:=

y = (2 - x)/(x^2 - 4)

Out[13]=

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

In[14]:=

Limit[y, x2]

Out[14]=

-1/4

In[16]:=

Plot[y, {x, -5, 2}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_27.gif]

43.

In[17]:=

Clear[y]

In[18]:=

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

Out[18]=

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

In[19]:=

Limit[y, x1]

Out[19]=

3/2

In[20]:=

Plot[y, {x, -5, 1}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_34.gif]

44.

In[21]:=

Clear[y]

In[23]:=

y = ((Sqrt[2 + x]) - Sqrt[2])/x

Out[23]=

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

In[24]:=

Limit[y, x0]

Out[24]=

1/(2 2^(1/2))

57.

In[25]:=

Clear[y]

In[28]:=

y = Sin[x]/(5x)

Out[28]=

Sin[x]/(5 x)

In[29]:=

Limit[y, x0]

Out[29]=

1/5

In[30]:=

Plot[y, {x, -2π, 2π}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_46.gif]

58.

In[31]:=

Clear[y]

In[32]:=

y = (3 (1 - Cos[x]))/x

Out[32]=

(3 (1 - Cos[x]))/x

In[33]:=

Limit[y, x0]

Out[33]=

0

In[34]:=

Plot[y, {x, -2π, 2π}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_53.gif]

59.

In[35]:=

Clear[y]

In[38]:=

y = (Sec[θ] - 1)/(θ Sec[θ])

Out[38]=

(Cos[θ] (-1 + Sec[θ]))/θ

In[39]:=

Limit[y, θ0]

Out[39]=

0

In[42]:=

Plot[y, {θ, -2π, 2π}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_60.gif]

60.

In[43]:=

Clear[y]

In[44]:=

y = Cos[θ] Tan[θ]/θ

Out[44]=

Sin[θ]/θ

In[45]:=

Limit[y, θ0]

Out[45]=

1

In[46]:=

Plot[y, {θ, -2π, 2π}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_67.gif]

61.

In[47]:=

Clear[y]

In[48]:=

y = (Sin[x]^2)/x

Out[48]=

Sin[x]^2/x

In[49]:=

Limit[y, x0]

Out[49]=

0

In[50]:=

Plot[y, {x, -2π, 2π}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_74.gif]

62.

In[51]:=

Clear[y]

In[52]:=

y = ((Tan[x])^2)/x

Out[52]=

Tan[x]^2/x

In[53]:=

Limit[y, x0]

Out[53]=

0

In[54]:=

Plot[y, {x, -2π, 2π}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_81.gif]

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