Calculus 1 question... I need help solving limit problems as it approaches infinity

[RaynorWolfcastle]

Originally posted by: fritolays
sorry to ask again but can someone help me out?

the questions is lim as x->infinity of squareroot of (9X+2) / 4X+3

the square root is just for the numerator

i graphed it and it looks like it is approaching 0 as x->0 but i want to see how it is done

also what about the lim as x> - infinity? (negative infinity)

think of it this way, how relevant are the +2 and +3 terms as you approach infinity? (hint: try doing (10,000,000 + 2) / (10,000,000 + 3)
so as you approach infinity in this case the addition terms' importance becomes nothing, so you're left with 9X/4X or 9/4.

This reasoning always works, even if the powers are different, that is if you have (9x^3 + 56x^2 + 78x - 5,000) / (4x + 1,023,423) then the important terms are the leading terms (ie the numerator term in x^3 and the denominator term in x). so you check lim 9x^3/4x and get that it tends to infinity.

Keep in mind that this technique only works for limits with the limit being infinity.

in your case the leading term in the numerator is smaller than the leading term in the denominator, so we know that the limit will be 0. The negative infinity limit on the other hand will also be 0, but only if you allow for the presence of imaginary numbers.