How do you find the limit of #sqrt(4x^2-1) / x^2# as x approaches #oo#?
1 Answer
Apr 25, 2016
Explanation:
Combine all the terms into the square root:
#lim_(xrarroo)sqrt(4x^2-1)/x^2=lim_(xrarroo)sqrt(4x^2-1)/sqrt(x^4)#
#=lim_(xrarroo)sqrt((4x^2-1)/x^4)=lim_(xrarroo)sqrt(((4x^2-1)/x^4)/(x^4/x^4))#
#=lim_(xrarroo)sqrt((4/x^2-1/x^4)/1)=lim_(xrarroo)sqrt(4/x^2-1/x^4)#
We can now evaluate the limit.
#=sqrt(0-0)=0#
