Do \(-1\le sinx\le1\) \(\forall x\Rightarrow\frac{-1}{n^3}\le\frac{sin\frac{n^2\pi}{3}}{n^3}\le\frac{1}{n^3}\)
Mà \(lim\frac{-1}{n^3}=lim\frac{1}{n^3}=0\)
\(\Rightarrow lim\frac{1}{n^3}.sin\frac{n^2\pi}{3}=0\) theo giới hạn kẹp
Chương 4: GIỚI HẠN
Các câu hỏi tương tự
limu_nleft(1-frac{1}{2^2}right)left(1-frac{1}{3^2}right)...left(1-frac{1}{n^2}right)
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Đọc tiếp
\(limu_n=\left(1-\frac{1}{2^2}\right)\left(1-\frac{1}{3^2}\right)...\left(1-\frac{1}{n^2}\right)\\
n\rightarrow\infty\)\(limu_n=n\left(\sqrt[3]{n^{\alpha}+1}-n\right)\\ n\rightarrow\infty\)\(lim\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}\\ x\rightarrow1\)\(lim\frac{\sqrt{2}-2\cos x}{4x-\pi}\\ x\rightarrow\frac{\pi}{4}\)\(lim\left(\sin\frac{1}{x}+\cos\frac{1}{x}\right)^x\\
x\rightarrow\infty\)\(lim\frac{x^{n+1}-\left(n+1\right)x+n}{\left(x-1\right)^2}\\ x\rightarrow1\)\(lim\left(1-x\right)\tan\frac{\pi x}{2}\\ x\rightarrow1\)\(lim\frac{\sqrt{\cos x}-\sqrt[3]{\cos x}}{\sin^2x}\\ x\rightarrow0\)\(lim\sqrt[x]{1-2x}\\ x\rightarrow0\)\(lim\left(\sin x\right)^{\tan x}\\ x\rightarrow\frac{\pi}{2}\)
tìm giới hanjn
1) lim \(\frac{\left(-1\right)^n}{n-3}\)
2) lim \(\frac{n\left(sin\left(pi.n^2\right)\right)}{n^2+3n-2}\)
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 \(\frac{2n+3}{\sqrt{9n^2+3}-\sqrt[3]{2n^2-8n^3}}\)
tìm giới hạn
\(\lim\limits_{x\rightarrow1}\frac{1+sin\pi x}{x+1}\)
a)lim \(\frac{\left(2n+1\right)^2\left(n-1\right)}{\sqrt[3]{n^3+7n-2}}\)
b)lim [(2n-1)\(\sqrt{\frac{2n^2+5}{n^4+n^2+2}}\)]
c)lim [n(\(\sqrt[3]{n^3+n^2}-n\))]
\\(\\lim\\limits_{x\\rightarrow8}\\frac{\\sqrt[3]{x}-2}{2x-16}\\)
\n\n\\(\\lim\\limits_{x\\rightarrow-2}\\frac{\\sqrt{x-3}-1}{\\sqrt[3]{x-6}+2}\\)
\n\n\\(\\lim\\limits_{x\\rightarrow1}\\frac{2x-1-\\sqrt{x^2+2x-2}}{x^2-4x+3}\\)
\nGiúp e 3 bài này với ạ 1, Lim sin^2n / n + 2 2, Lim 1 + cosn / 2n + 3 3, Lim cosn + 4 / 5 + n
cho f(n) = \(\frac{1}{\sqrt[3]{2}}+\frac{1}{\sqrt[3]{3}}+\frac{1}{\sqrt[3]{4}}+...+\frac{1}{\sqrt[3]{n}}\) nϵN*. GIá trị lim\(\frac{f\left(n\right)}{n^2+1}\) bằng ?
Tìm \(\lim\limits_{x->-\infty}\)\(\frac{\left|x\right|\sqrt{4x^2+3}}{2x-1}\)
lim \(\sqrt{n}\)(\(\sqrt{n+4}\)-\(\sqrt{n+3}\))
lim (n-2-\(\sqrt{3n^2+n-1}\))
\(\lim\limits_{x->0}\)\(\frac{\sqrt[3]{x^3-2x+1}-1}{x^2+2x}\)