How do you evaluate the limit #(x^-1-2)/(x-1/2)# as x approaches #1/2#?
1 Answer
Aug 12, 2016
Explanation:
We have the limit:
#lim_(xrarr1/2)(x^-1-2)/(x-1/2)=lim_(xrarr1/2)(1/x-2)/(x-1/2)#
#=lim_(xrarr1/2)(1/x-2)/(x-1/2)*((2x)/(2x))#
#=lim_(xrarr1/2)(2-4x)/(2x^2-x)#
#=lim_(xrarr1/2)(2(1-2x))/(x(2x-1))#
#=lim_(xrarr1/2)(-2(2x-1))/(x(2x-1))#
#=lim_(xrarr1/2)(-2)/x#
#=(-2)/(1/2)#
#=-4#
