Question

Find the lim as x approaches - infinity 4x+2/sqrt(9x^2+2x-3) = -4/3
can someone show me how to get this answer without using L'hopitals rule...

Answer 1

because the denominator limit under the root makes it indeterminant,you have to use L,Hospital's

Answer 2

any time a rational number takes on 0/0, n/0, infty/infty, you can use L'Hospital's and find a reasonable limit answer, but in each of those cases it is impossible to do other techniques often than not, unless it is possible to prove it by squeeze theorem, but not in this case