How to Evaluate the limit as x approaches 0 of ln of the quantity 1 minus x squared close quantity over x.

Answer 1

ln(1-x^2)/x

find limit as x approaches zero

plug in zero, but that leads to an undefined value: 0/0

so use L'Hopital's rule

take derivatives separately of numerator and denominator

-2x/(1-x^2)= (-2)(0)/(1-0^2)

=0/1=0

or just graph y = ln(1-x^2)/x with a graphing calculator

and see where y is when x=0. it's the origin (0,0)