Please help me with Lim excercise and explain it as well? Really appreciate!

Question

Charles Arocha · Accepted Answer

Assuming #nrarroo#, we have #a = 1#.

#lim_(nrarroo)[sqrt(2n^2+n)-asqrt(2n^2-n)]# Observe that if #a = -1#, then the limit is #oo# (not real). So we know that #a != -1# Rewrite. Multiply by #(sqrt(2n^2+n)+asqrt(2n^2-n))/(sqrt(2n^2+n)+asqrt(2n^2-n))# to get: #sqrt(2n^2+n)-a^2sqrt(2n^2-n) = ((2n^2+n)-a^2(2n^2-n))/(sqrt(2n^2+n)+a^2sqrt(2n^2-n))# # = (2n^2(1-a^2)-n(1+a^2))/ (n(sqrt(2+1/n)+a^2sqrt(2-1/n))# # = (2n(1-a^2)-(1+a^2))/ (sqrt(2+1/n)+a^2sqrt(2-1/n)# Now if #1-a^2 != 0#, then the limit is #oo# (not real). So #1-a^2 = 0#. We already ruled out #-1#, so we must have #a = 1#

Ezekiel Alexander · Answer

undefined Sure, I'd be happy to help you with a limit exercise. Could you please provide me with the specific problem or question you need assistance with?