1) The limit to 5/3+2e^-x as x goes to infinity is found by seeing what happens as e^-x or 1/(e^x) goes to infinity. If you know that e^x goes to infinity as x goes to infinity (which you should by the graph of e^x) then you know that e^-x approaches 0 as x goes to infinity. That also cancels out the 2. So your final answer is 5/3.
2) The limit to 5/3+2e^-x as x goes to -infinity is infinity. So the total limit is infinity.
Comments
Hi,
lim 5/3+2e^-x = 5/3 + 0 = 5/3
x-> ∞
lim 5/3+2e^-x = 5/3 + 2e^(positive exponent from -(negative x)) = ∞
x->-∞
I hope that helps!! :-)
1) The limit to 5/3+2e^-x as x goes to infinity is found by seeing what happens as e^-x or 1/(e^x) goes to infinity. If you know that e^x goes to infinity as x goes to infinity (which you should by the graph of e^x) then you know that e^-x approaches 0 as x goes to infinity. That also cancels out the 2. So your final answer is 5/3.
2) The limit to 5/3+2e^-x as x goes to -infinity is infinity. So the total limit is infinity.