limit's help question.. work shown... need help!

[johnq2k7]

Explain why the limit :

lim (x--> negative infinity) cos^-1 {(3-x)/(x+4)} is not well defined?

Work shown:

I'm not sure why it is stated as not well defined because when i use the strategy of dividing the expression within the brackets of the inverse cosine expression i get:

cos^-1 { [(3/x)-(x/x)]/ [(x/x)+(4/x)]}

and since 1/x as x--> negative infinity is equal to zero (I think this assumption might be wrong)

therefore limit of x---> negative infinity of cos^-1 {(3-x)/(x+4)}= 180 or Pi

I didn't end up with undefined quantity or limit.. what did I do wrong.. please help

 

[Deleted member 4993]

Explain why the limit :

lim (x--> negative infinity) cos^-1 {(3-x)/(x+4)} is not well defined?

Work shown:

I'm not sure why it is stated as not well defined because when i use the strategy of dividing the expression within the brackets of the inverse cosine expression i get:

cos^-1 { [(3/x)-(x/x)]/ [(x/x)+(4/x)]}

and since 1/x as x--> negative infinity is equal to zero (I think this assumption might be wrong)

therefore limit of x---> negative infinity of cos^-1 {(3-x)/(x+4)}= 180 or Pi

I didn't end up with undefined quantity or limit.. what did I do wrong.. please help

Let us look at the graph of (3-x)/(4+x)

Does it have a horizontal asymptote?

Do you see any problem with having a arc_cosine of this function? What is the absolute maximum value of cosine?

 

[johnq2k7]

Explain why the limit :

lim (x--> negative infinity) cos^-1 {(3-x)/(x+4)} is not well defined?

Work shown:

I'm not sure why it is stated as not well defined because when i use the strategy of dividing the expression within the brackets of the inverse cosine expression i get:

cos^-1 { [(3/x)-(x/x)]/ [(x/x)+(4/x)]}

and since 1/x as x--> negative infinity is equal to zero (I think this assumption might be wrong)

therefore limit of x---> negative infinity of cos^-1 {(3-x)/(x+4)}= 180 or Pi

I didn't end up with undefined quantity or limit.. what did I do wrong.. please help

Let us look at the graph of (3-x)/(4+x)

Do you see any problem with having a arc_cosine of this function? What is the absolute maximum value of cosine?

The absolute maximum value of cosine is 1 and the minimum value is -1.......

but the arccosine value can be 180 degrees or pi right.. i'm still confused.. so is this value undefined