March 10, 2006 5:25 am
Larson ch 1.3, p. 64 - 66
63.

In[1]:=

y = ((1 - Cos[h])^2)/h

Out[1]=

(1 - Cos[h])^2/h

In[2]:=

Limit[y, h0]

Out[2]=

0

In[3]:=

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

[Graphics:HTMLFiles/index_6.gif]

64.

In[4]:=

Clear[y]

In[7]:=

y = ϕ (Sec[ϕ])

Out[7]=

ϕ Sec[ϕ]

In[8]:=

Limit[y, ϕπ]

Out[8]=

-π

In[9]:=

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

[Graphics:HTMLFiles/index_13.gif]

In[10]:=

Plot[y, {ϕ, 2, 4}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_15.gif]

65.

In[11]:=

Clear[y]

In[12]:=

y = Cos[x]/Cot[x]

Out[12]=

Sin[x]

In[13]:=

Limit[y, xπ/2]

Out[13]=

1

In[14]:=

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

[Graphics:HTMLFiles/index_22.gif]

66.

In[15]:=

Clear[y]

In[16]:=

y = (1 - Tan[x])/(Sin[x] - Cos[x])

Out[16]=

(1 - Tan[x])/(-Cos[x] + Sin[x])

In[17]:=

Limit[y, xπ/4]

Out[17]=

-2^(1/2)

In[18]:=

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

[Graphics:HTMLFiles/index_29.gif]

In[19]:=

Plot[y, {x, -2π, π/4}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_31.gif]

In[20]:=

Plot[y, {x, -1, π/4}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_33.gif]

67.

In[21]:=

Clear[y]

In[22]:=

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

Out[22]=

Sin[t]^2/t^2

In[23]:=

Limit[y, t0]

Out[23]=

1

In[25]:=

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

[Graphics:HTMLFiles/index_40.gif]

85.

In[26]:=

Clear[y]

In[29]:=

f = x

Out[29]=

x

In[30]:=

g = Sin[x]

Out[30]=

Sin[x]

In[31]:=

h = Sin[x]/x

Out[31]=

Sin[x]/x

In[36]:=

p1 = Plot[f, {x, -2π, 2π}, PlotStyleGreen] ;

[Graphics:HTMLFiles/index_49.gif]

In[35]:=

p2 = Plot[g, {x, -2π, 2π}, PlotStyleRed] ;

[Graphics:HTMLFiles/index_51.gif]

In[37]:=

p3 = Plot[h, {x, -2π, 2π}, PlotStyleBlue] ;

[Graphics:HTMLFiles/index_53.gif]

In[39]:=

Show[p1, p2, p3] ;

[Graphics:HTMLFiles/index_55.gif]

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