March 08, 2006 5:15 am
Larson ch 1.3, p. 64 - 66
23.

In[1]:=

y = Sec[2x]

Out[1]=

Sec[2 x]

In[2]:=

Limit[y, x0]

Out[2]=

1

In[3]:=

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

[Graphics:HTMLFiles/index_6.gif]

24.

In[4]:=

Clear[y]

In[13]:=

y = Cos[3x]

Out[13]=

Cos[3 x]

In[14]:=

Limit[y, xπ]

Out[14]=

-1

In[16]:=

Plot[y, {x, 0, 3π}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_13.gif]

25.

In[17]:=

Clear[y]

In[18]:=

y = Sin[x]

Out[18]=

Sin[x]

In[19]:=

Limit[y, x5π/6]

Out[19]=

1/2

In[20]:=

Plot[y, {x, 0, 5π/6}, PlotStyle Red] ;

[Graphics:HTMLFiles/index_20.gif]

In[21]:=

Sin[π/6]

Out[21]=

1/2

In[22]:=

Plot[Sin[x], {x, 0, 2π}, PlotStyleBlue]

[Graphics:HTMLFiles/index_24.gif]

Out[22]=

⁃Graphics⁃

26.

In[23]:=

Clear[y]

In[24]:=

y = Cos[x]

Out[24]=

Cos[x]

In[25]:=

Limit[y, x5π/3]

Out[25]=

1/2

In[27]:=

Plot[y, {x, 0, 5π/3}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_32.gif]

In[28]:=

Cos[5π/3]

Out[28]=

1/2

In[29]:=

Cos[π/6]

Out[29]=

3^(1/2)/2

27.

In[30]:=

Clear[y]

In[31]:=

y = Tan[(π) x/4]

Out[31]=

Tan[(π x)/4]

In[32]:=

Limit[y, x3]

Out[32]=

-1

In[34]:=

Plot[y, {x, 0, 3π/4}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_43.gif]

28.

In[36]:=

Clear[y]

In[37]:=

y = Sec[(π) x/6]

Out[37]=

Sec[(π x)/6]

In[38]:=

Limit[y, x7]

Out[38]=

-2/3^(1/2)

In[39]:=

Plot[y, {x, 0, 7π/6}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_50.gif]

37.

In[40]:=

Clear[y]

In[41]:=

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

Out[41]=

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

In[42]:=

Limit[y, x -1]

Out[42]=

-2

In[43]:=

Plot[y, {x, -5, 5}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_57.gif]

38.

In[44]:=

Clear[y]

In[45]:=

y = (2x^2 - x - 3)/(x + 1)

Out[45]=

(-3 - x + 2 x^2)/(1 + x)

In[46]:=

Limit[y, x -1]

Out[46]=

-5

In[48]:=

Plot[y, {x, -5, 5}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_64.gif]

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