a) lim ( x tends to 2 ) 1 / ( x - 2 )

b) lim (x tends to 2) 1/ (x-2)^2

I would be grateful if you can help me with this, providing clear explanations

Thanks in advance!

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- September 3rd 2008, 12:04 AMose90Limit of a function as x tends to real number
a) lim ( x tends to 2 ) 1 / ( x - 2 )

b) lim (x tends to 2) 1/ (x-2)^2

I would be grateful if you can help me with this, providing clear explanations

Thanks in advance! - September 3rd 2008, 12:11 AMProve It
- September 3rd 2008, 12:22 AMose90
Good explanation , thanks!

However, the answer shown in my notes for a) is no limit, is it obviously wrong? - September 3rd 2008, 12:32 AMMoo
Yes.

Consider x to 2, with x>2 (from the right). Then x-2>0.

So it will be**positive**infinity.

Consider x to 2, with x<2 (from the left). Then x-2<0.

So it will be**negative**infinity.

Thus

This means the limit doesn't exist, because the limit is not the same from the right and from the left. - September 3rd 2008, 01:51 AMmr fantastic
It's essential that left hand and right and right hand limits are always considered.

It's not good enough to say x - 2 --> 0 etc.

You need to consider and , whether the limiting value of x - 2 etc. is or and consequently whether the left and right handed limits are +oo or -oo .... - September 3rd 2008, 03:02 AMose90
Thanks everyone, I have understood.