Hi, is it possible to evaluate 1/(x-1) at x=1 by any means?
Thanks
As x gets closer and closer to 1, the numerator remains 1 while the denominator gets closer and closer to 0- the entire fraction (in absolute value) gets larger and larger- there is NO limit.
You can't even say "$\displaystyle \displaytype\lim_{x\to 1}\frac{1}{x- 1}= \infty$".
If x< 1, the denominator is negative so $\displaystyle \displaytype\lim_{x\to 1^-}\frac{1}{x- 1}= -\infty$.
If x> 1, the denominator is positive so $\displaystyle \displaytype\lim_{x\to 1^+}\frac{1}{x- 1}= \infty$.