Exponential Limits

This is given a^x and b^x, like for example, 3^x and e^x.

If a > b, what is the limit?

infinity

If a < b, what is the limit?

0

If a = b, what is the limit?

1

SOLVE: Find the limit of 3^x/e^x

infinity, because 3 > 2.71 (e)

If a^x/b^x is negative, what is the limit?

This is indeterminate.

SOLVE: Find the limit of 3^x/e^2x

0, because e²^x = (e²)^x and e² > 3.

You're comparing two exponentials. Which one is greater: x^y or y^x?

If both values are larger than e, the number with the higher exponent value is greater. If both values are smaller than e, the number with the smaller exponent value is greater.

Which one is greater: pi^3.14 or 3.14^pi?

3.14^pi because the numbers are both greater than e