show which function grows faster.. as x approaches infinity..

e^x , e^cosx

e^x , sqrt(1 + x^4)

I understand the concept, but am having a hard time with the e^x. How do I go at these?

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- Jan 11th 2010, 05:27 PMMorgan82relative rates of growth
show which function grows faster.. as x approaches infinity..

e^x , e^cosx

e^x , sqrt(1 + x^4)

I understand the concept, but am having a hard time with the e^x. How do I go at these? - Jan 11th 2010, 05:52 PMpickslides
I believe $\displaystyle e^x > \sqrt{1 + x^4}> e^{cosx} , x \rightarrow \infty$