Arithmetic with Large and Small Numbers

• 1. If 0 < x < 1, then is 5/x less than or greater than 5 ?

  2. If 0 < x < 1, then is 0.01/x less than or greater than 0.01?

  3. If 0 < x < 1, then is x^9 less than or greater than x?

  4. If 0 < x < 1, then is x(1.01) less than or greater than 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) ?

Updated: 31 August, 2009 17:44:19