\(\sqrt{\frac{4n-2}{n+5}}\)
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Những câu hỏi liên quan
Tính \(\frac{\sqrt{m}-2\sqrt{n}+2014}{4-\sqrt{m}-2\sqrt{5}}\),biết \(m+4\sqrt{mn}-2\sqrt{m}-4\sqrt{n}+4n=3\)
Giúp mình giải với
a) lim \(\frac{\sqrt{n^2-4n}-\sqrt{4n+1}}{\sqrt{3n^2+1}+n}\)
b)lim \(\frac{\sqrt[3]{8n^3+n^2}-n}{2n-3}\)
a)lim \(\frac{\sqrt{n^2-4n}-\sqrt{4n+1}}{\sqrt{3n^2+1}+n}\)
=lim \(\frac{\sqrt{1-\frac{4}{n}}-\sqrt{\frac{4}{n}+\frac{1}{n^2}}}{\sqrt{3+\frac{1}{n^2}}+1}=\frac{1}{\sqrt{3}+1}\)
b)lim \(\frac{\sqrt[3]{8n^3+n^2}-n}{2n-3}\)
= lim \(\frac{\sqrt[3]{8+\frac{1}{n^3}}-1}{2-\frac{3}{n}}=\frac{2-1}{2}=\frac{1}{2}\)
lim
\(lim\frac{\sqrt{4n^2+1}+2n-1}{\sqrt{n^2+4n+1}+n}\)
\(lim\frac{\sqrt{4n^2+1}+2n-1}{\sqrt{n^2+4n+1}+n}\)
= \(lim\frac{\sqrt{4+\frac{1}{n^2}}+2-\frac{1}{n}}{\sqrt{1+\frac{4}{n}+\frac{1}{n^2}}+1}\)
=\(\frac{2+2}{1+1}=2\)
lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
lim \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\)
lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
a) lim \(\frac{\left(2n^2-3n+5\right)\left(2n+1\right)}{\left(4-3n\right)\left(2n^2+n+1\right)}\)
= lim \(\frac{\left(2-\frac{3}{n}+\frac{5}{n^2}\right)\left(2+\frac{1}{n}\right)}{\left(\frac{4}{n}-3\right)\left(2+\frac{1}{n}+\frac{1}{n^2}\right)}=\frac{4}{-6}=-\frac{2}{3}\)
b)lim ( \(\frac{\sqrt{n^4+1}}{n}-\frac{\sqrt{4n^6+2}}{n^2}\))
= lim ( \(\frac{n\sqrt{n^4+1}-\sqrt{4n^6+2}}{n^2}\) )
= lim \(\frac{\left(n^6+n^2\right)-\left(4n^6+2\right)}{n^2\left(n\sqrt{n^4+1}+\sqrt{4n^2+2}\right)}\)
= lim \(\frac{-3n^6+n^2+2}{n^3\sqrt{n^4+1}+n^2\sqrt{4n^2+2}}\)
= lim \(\frac{-3n\left(1-\frac{1}{n^4}-\frac{2}{n^6}\right)}{\sqrt{1+\frac{1}{n^4}}+\frac{1}{n^2}\sqrt{4+\frac{2}{n^2}}}\)
= lim \(-3n=-\infty\)
c) lim \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
= lim\(\frac{2+\frac{3}{n}}{\sqrt{9+\frac{3}{n^2}}-\sqrt[3]{\frac{2}{n}-8}}=\frac{2}{3+2}=\frac{2}{5}\)
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tìm \(n\varepsilonℕ^∗\)để \(\sqrt{\frac{4n-2}{n+5}}\varepsilonℚ\)
5/ lim \(\frac{\left(12-n\right)^3\left(n-2\right)}{\sqrt{n^8-1}-2n^4}\)
6/ lim \(\frac{\sqrt[3]{3-8n^3}-n}{2n+5}\)
7/ lim \(\frac{\sqrt{n^6-2n+1}}{\sqrt{4n^6+3n}}\)
8/ lim \(\left(n^4+2n-20\right)\)
\(\sqrt{4n+1}-\sqrt{4n}>\frac{1}{\sqrt{n+1}}\)
lim\(\sqrt{n^{4^{ }}-n^2+1}\) +2n2
lim\(\sqrt{n^4-n^2+1}\) -2n2
lim \(\frac{3n^2+n-5}{2n^2+1}\)
lim\(\frac{\sqrt{9n^2-n}+1}{4n-2}\)
lim\(\frac{3n^2+n-5}{2n^2+1}\)=lim\(\frac{n^2\left(3+\frac{1}{n}-\frac{5}{n^2}\right)}{n^2\left(2+\frac{1}{n}\right)}\)=\(\frac{3}{2}\)
lim\(\frac{\sqrt{9n^2-n}+1}{4n-2}\)=lim\(\frac{n\sqrt{9-\frac{1}{n}+\frac{1}{n^2}}}{n\left(4-\frac{2}{n}\right)}\)=lim\(\frac{\sqrt{9}}{4}\)=\(\frac{3}{2}\)
Giúp mk lm bài này nha mấy bạn: Cho f(n)=\(\frac{4n+\sqrt{4n^2-1}}{\sqrt{2n+1}+\sqrt{2n-1}}\) với n nguyên dương. Hãy tính giá trị của tổng: f(1)+f(2)+f(3)+..........+f(40)
