Find intervals containing solutions to(adsbygoogle = window.adsbygoogle || []).push({});

[tex] 4x^2 - e^x = 0 [/tex]

well someone suggested i sketch the graphs of 4x^2 and 2^x but im not sure on how to go past that point...

All i have to do is find the intervals so do the intersection point(s) of these two functions indicate the intervals where the roots may exist?

Find the Rates of convergence of the following sequences are n -> infinity

a) [tex] \lim_{n\rightarrow\infty} \sin{\frac{1}{n}} = 0 [/tex]

i was wondering if expanding the sine by taylor series would help the case.. and if that is so, at which term would i stop at?

b) [tex] \lim_{n\rightarrow\infty} \sin{\frac{1}{n^2}} = 0 [/tex]

c) [tex] \lim_{n\rightarrow\infty} (\sin{\frac{1}{n}})^2 = 0 [/tex]

d) [tex] \lim_{n\rightarrow\infty} \ln{(n+1)}-\ln{n}= 0 [/tex]

the last one looks like ln((n+1)/n) which i think can be expanded by taylor series... if this is the right idea please do tell.

ALso what is the taylor series about.. as in what is the x0 value and the c value where c is the n+1 derivative's evaltuation point.

any help that you could provide for these would be greatly appreicated!!

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# Homework Help: Numerical methods

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