Arrange the functions x^1/2, x^2, x^3, and 2^x by relative sizes of their y-values a.On (1, ∞) Note that some of the functions change their relative positions on this interval. Which one ultimately surpasses the others?

Question

anonymous · Answer

2^x will grow faster than all of them in the limit as x-> infinity (gets very large).

anonymous · Answer

For example plug in 1000. You get:
x^(1/2) = 31.62277660168379331998893544432718533719555139325216826857504...
x^2 = 10^6 = 1000000
x^3 = 10^9 = 1000000000
2^x = 10715086071862673209484250490600018105614048117055336074437503883703510511249361224931983788156958581275946729175531468251871452856923140435984577574698574803934567774824230985421074605062371141877954182153046474983581941267398767559165543946077062914571196477686542167660429831652624386837205668069376

anonymous · Answer

Significant difference there. :)