Try to do these problems first without a calculator, then check your answers using a calculator. These problems are to help you with finding limits, which we will be doing a lot of for the rest of the semester.

1. If 0 < x < 1, then  5/x  is  > 5  or < 5 ?

2. If 0 < x < 1, then  0.01/x  is  > 0.01  or < 0.01 ?

3. If 0 < x < 1, then  x^9  is  > x or < x ?

4. If 0 < x < 1, then  x(1.01)  is  > x  or < x ?

5. Is (1.01)^2  less than or greater than 1.01 ?

6. As x --> infinity, (1.01)^x --> ?

7. Is (0.99)^2  less than or greater than 0.99 ?

8. As x --> infinity, ( 0.99)^x --> ?

9. Is 5^(0.00001) close to 0, or close to and less than 1, or close to and greater than 1?

10. As x --> infinity, x^(0.00001) --> ?

11. As x --> infinity, 100000^(1/x) --> ?

12. True or False:  if L is large, and S is small (positive and close to zero), then LS is close to zero.

13. True or False:  if L is large, and S is small (positive and close to zero), then L^S is close to one.

14. True or False:  if L is large, and S is small (positive and close to zero), then S^L is close to zero.
     

15. As x --> infinity, which is larger: (x^2 - 100x) or (100x + 10000) ?

16. As x --> infinity, which is larger: x^2 or 2^x or e^x ?

17. As x --> infinity, which is larger: x^2000 or (1.001)^x ?

18. As x --> infinity, which is larger: 1/x^2 or e^(-x) ?

19. As x --> infinity, which is larger: sqrt(x) or ln(x) ?

20. As x --> infinity, which is larger: x^(0.0001) or ln(x) ?