x | 1 | 8 | 27 | 64 |
y | 1 | 2 | 3 | 4 |
x | -1 | -8 | -27 | -64 |
y | -1 | -2 | -3 | -4 |
2) If lim f(x) = 0 and lim g(x) = 0, try one of the following:
b)
If f(x) or g(x) involves a square root, multiply both the numerator and
the denominator by the conjugate of the square root expression.
b) lim doesn't exist.
5) If all else fails, get out the calculator and crunch the numbers. If x approaches infinity or negative infinity use very large or very small values and watch the pattern develop. If the limit approaches a number c, then use numbers close to c on both sides of c.
x | .1 | .01 | .001 | -.1 | -.01 | -.001 |
y | 11 | 101 | 1001 | -9 | -99 | -999 |
2) f(c) must exist.
3) Statement one must = statement two!
doesn't exist. f(c) doesn't exist.................................... f(c)