Evaluate the following limits by constructing the table of values.

Question

2. lim 5^x

^x->3

Answer 1

Hey!

Try some values that are really "close" on both sides of 3. These need to be approaching from both directions - on the left and right. For example, you could try 3.001, 3.002,... on the right, or the 'positive side,' and ...2.998, 2.999 on the 'negative' side.

After evaluating the limit for x on both sides (using at least a few points on each side), it should be easy to see what the limit is approaching for f(x). (This is important because f(3) isn't necessarily the limit of the function. It could easily diverge as it approaches 3 from either direction.)

Let me know if you have questions!