1. Substitute the number being approached into the variable. If you get a number other than 0, then you have found your limit. SubstitutionFactor Factor out the denominator and the numerator. See if you can eliminate any “like” terms. If you can, cancel them out, and then plug in the limit that is being approached into the new equation. Eliminate Complex Fractions If you have complex fraction, multiply the numerator and the denominator by the common denominator.

2. Multiply By The Conjugate If you have a square root in the numerator, multiply by it’s conjugate to eliminate the square root. Infinity Limits 3 cases: 1.) highest power in numerator < highest power in denominator LIMIT = 0 2.) highest power in numerator > highest power in denominator LIMIT = infinity 3.) highest power in numerator = highest power in denominator LIMIT = ratio of the coefficients Use Logic Use your common sense. If you have an infinity limit, try plugging in infinity. See if the numerator is bigger than the denominator. #/huge = 0 #/small = infinity

3. Make A Big Square Root When you have a square root in the denominator, square the top so you can make the problem into a BIG SQUARE ROOT. Synthetic Division When you have two polynomials in the numerator and denominator, see if you can use synthetic division to simplify the fraction. When none of the methods work… use the greatest integer function. Greatest Integer Function