Suppose lim x→1 (sqrt(ax+b)-2)/(x-1)=1, then a-b = ?

The answer key solved this by seeing the limit as 0/0, and therefore, sqrt(ax+b)-2 as 0.

What's the assumption, sqrt(ax+b)-2=0, based on?

Thanks in advance!

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- Mar 22nd 2013, 09:33 AMLLLLLLAn indeterminate limit question
Suppose lim x→1 (sqrt(ax+b)-2)/(x-1)=1, then a-b = ?

The answer key solved this by seeing the limit as 0/0, and therefore, sqrt(ax+b)-2 as 0.

What's the assumption, sqrt(ax+b)-2=0, based on?

Thanks in advance! - Mar 22nd 2013, 10:24 AMSironRe: An indeterminate limit question
If you substitute the value in the limit then the denominator is equal to . This means the numerator can't be equal to some as the limitvalue would be infinite then (i.e it would not exist). Hence the only possibility is that the numerator is equal to as is undefined.