Estimating+limits+from+graphs+or+tables+using+data

=__Estimating Limits from Graphs and Data Tables__= Direct substitution works for most range values, but not infinity and negative infinity. Also, all limit values can be obtained from analyzing a table of values very close to a value, but not the value itself. The values infinitely close to the domain value will produce the limit from the direction the domain value is obtained from.

Example: What is the limit as x approaches 2? Answer: positive infinity
 * x || 1.9 || 1.99 || 2 || 2.01 || 2.1 || 2.2 ||
 * F(x) || 43453 || 6435745 || undefined || 76547576 || 45345 || 3453 ||

Example 2: What is the limit as x approaches 3? Answer: 3
 * x || 2.9 || 2.99 || 3 || 3.01 || 3.1 || 3.2 ||
 * F(x) || 2.97 || 2.999 || undefined || 3.0001 || 3.01 || 3.1 ||

Example 3: What is the limit as x approaches 4? Answer: does not exist because the function approaches infinity from the left and negative infinity from the right.
 * x || 3.9 || 3.99 || 4 || 4.01 || 4.1 || 4.2 ||
 * F(x) || 634643 || 12341552 || undefined || -24312412 || -54245 || -543 ||