Friday, 11 September 2015

real analysis - Limit of nsqrtn2+2n

bn=nn2+2n. Taking (1n)0 as given, using Algebraic Limit Theorem, show lim exists and find value



The question also says to use the fact that if (x_n)\rightarrow x then \sqrt{x_n}\rightarrow \sqrt{x}. I've simplified the {b_n} down to n(1-\sqrt{1+\frac{2}{n}}), which appears to be going to zero as n gets large using the algebraic limit theorem. However, I know that \lim{b_n} = -1. I'm stuck on how to prove this, and I haven't found any help elsewhere. Any advice would be helpful!

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real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

How to find \lim_{h\rightarrow 0}\frac{\sin(ha)}{h} without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...