How do you find #lim (x-1)/(x-2sqrtx+1)# as #x->1^+#?

1 Answer
Mar 2, 2017

See below.

Explanation:

#(x-1)/(x-2sqrtx+1) = ((sqrtx+1)(sqrtx-1))/(sqrtx-1)^2#

# = (sqrtx+1)/(sqrtx-1)# #" "# for #x != 1#

#lim_(xrarr1^+) (x-1)/(x-2sqrtx+1) = lim_(xrarr1^+) (sqrtx+1)/(sqrtx-1)#

# = 2/0^+ = oo#

The notation in the last line is intended to indicate that the numerator approaches #2# and the denominator goes to #0# through positive values.
The result is a quotient that is increasing without bound.