Evaluate the following limits.

Question

lim as x approaches infinity 6/e^x + 7=____?

lim as x approaches negative infinity 6/e^x+7=____?

Answer 1

for the first
as x gets larger, 6/e^x gets closer to zero
so the limit is 0+7 = 7

for the second, remember that 1/a^-n = a^n

so for huge negative values of x, 6/e^x becomes "huge"
so for the second, it is undefined (infinitely large)