Question

Evaluate the limit as x approaches 1 of the quotient of the square root of the quantity x squared plus 3 minus 2 and the quantity x minus 1. You must show your work to receive credit.

Answer 1

A graph shows the limit to be 1/2.
https://www.desmos.com/calculator/qrf6ay47tw

Since the value of the function is the indeterminate form 0/0, L'Hôpital's rule applies. The ratio of derivatives of numerator and denominator is
.. x/$\sqrt{x^{2}+3 }$
Evaluated at x=1, this is
.. 1/$\sqrt{1^{2}+3 }$ = 1/2