 Page 2  The limiting value can be +∞ or -∞ For an ordinary polynomial, this will give a limit of infinity: 
or negative infinity:  because the highest power is odd. What happens when the argument is a fraction? Numerator is a Constant: 
If the limit is either positive or negative infinity, the denominator becomes infinitely large compared to the numerator, so the fraction's limiting value will be zero. The rule: 
The example above is just a special case of arguments that are made up of expressions in both the numerator and the denominator. The key to working out the limit is which has the higher degree, the top or the bottom!  The limit is 0 because the bottom (higher degree) gets to infinity faster than the top (lower degree).  Here the limit is infinity because the numerator's degree is larger; it gets to infinity faster than the denominator. If the numerator has the higher degree, the limit is infinity. If the denominator has the higher degree, the limit is zero. [Watch out for expressions that are out of order!] What happens if top and bottom have the same degree? Go on to page 3 ... |