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Tobal

Guest

Finding limits of indetermined forms WITHOUT L'Hopitals Rule

I need help finding limits of indetermined forms WITHOUT L'Hopitals Rule:

[img]Finding limits of indetermined forms WITHOUT L'Hopitals Rule[/img]

Please dont just give me the answer, I'd like to know how to do it. Thanks !

Tobal

Guest

Re: Finding limits of indetermined forms WITHOUT L'Hopitals Rule

Sorry

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: Finding limits of indetermined forms WITHOUT L'Hopitals Rule

Hi Tobal
For the first limit we have:
lim sqrt(x+6) + x  does not exist since the function is undefined for all x<-6
x ⇒-6-
lim sqrt(x+6) + x=0+(-6)=-6
x ⇒-6+

rzaidan

Member

Registered: 2009-08-13

Posts: 59

Re: Finding limits of indetermined forms WITHOUT L'Hopitals Rule

Hi Tobal
for the first function :
The left handside is -∞ and the right handside is  ∞ so the limit does not exist.
for the second function :
The left handside is ∞ and the right handside is  - ∞ so the limit does not exist.
for the third function :
Both left and right limits are ∞ since the denominator is squared.
for the forth function :
The left handside is ∞ and the right handside is  - ∞ so the limit does not exist.
to see the forth
the sign of the denominator when x is less and close to 1  is +ve
and the sign of the denominator when x is greater  and close to 1  is -ve so the two limits do not concide and the limit does not exist , and so for the rest functions
Best Wishes
Riad Zaidan