Chương 4: GIỚI HẠN
Các câu hỏi tương tự
tínha.limlimits_{n-+infty}dfrac{n^5+n^2-n+2}{left(2n^3-1right)left(n^2+n+1right)}b.limlimits_{n-+infty}dfrac{sqrt{n^2-n+2}}{n+2}c.limlimits_{n-+infty}dfrac{n-sqrt[3]{n^2-n^3}}{n^2+n+1}d.limlimits_{n-+infty}left(n-sqrt{n^2+n+1}right)
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tính
a.\(\lim\limits_{n->+\infty}\dfrac{n^5+n^2-n+2}{\left(2n^3-1\right)\left(n^2+n+1\right)}\)
b.\(\lim\limits_{n->+\infty}\dfrac{\sqrt{n^2-n+2}}{n+2}\)
c.\(\lim\limits_{n->+\infty}\dfrac{n-\sqrt[3]{n^2-n^3}}{n^2+n+1}\)
d.\(\lim\limits_{n->+\infty}\left(n-\sqrt{n^2+n+1}\right)\)
tính giới hạn
1.\(\lim\limits\left(n^3+4n^2-1\right)\)
2.\(lim\dfrac{\left(n+1\right)\sqrt{n^2-n+1}}{3n^2+n}\)
3.\(lim\dfrac{1+2+....+n}{2n^2}\)
4.\(lim\dfrac{3^n-4.2^{n-1}-10}{7.2^n+4^n}\)
1 a,Limsqrt{1+2n-n^3}b,Limsqrt{n^2+2n+3}-sqrt[3]{n^2+n^3}c,Limdfrac{left(2sqrt{n}+1right)left(sqrt{n}+3right)}{left(n+1right)left(n+2right)}d,dfrac{4^{n+1}-3times2^n}{3^{n+2}+2^n}e,dfrac{7^{n+1}-5^{n+2}+3}{2times6^{n+1}-3^n+3}f,dfrac{sqrt{n^4+1}}{n} -dfrac{sqrt{4n^6+1}}{n}
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1
a,Lim\(\sqrt{1+2n-n^3}\)
b,Lim\(\sqrt{n^2+2n+3}-\sqrt[3]{n^2+n^3}\)
c,Lim\(\dfrac{\left(2\sqrt{n}+1\right)\left(\sqrt{n}+3\right)}{\left(n+1\right)\left(n+2\right)}\)
d,\(\dfrac{4^{n+1}-3\times2^n}{3^{n+2}+2^n}\)
e,\(\dfrac{7^{n+1}-5^{n+2}+3}{2\times6^{n+1}-3^n+3}\)
f,\(\dfrac{\sqrt{n^4+1}}{n}\) -\(\dfrac{\sqrt{4n^6+1}}{n}\)
tính các giới hạn sau :a/ \(lim\dfrac{3x^2 3}{x 1}\left(x\rightarrow1\right)\)b/ \(lim\dfrac{2^n 2.4^n}{4.4^n-3.2^n}\)c/ \(lim\dfrac{\left(2n^2 1\right)\left(2n^5 n\right)}{n^7 2}\)d/ \(lim\dfrac{2x 1}{\left(x-2\right)^2}\left(x\rightarrow2\right)\)e...
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Tìm giới hạn các dãy số saua) limdfrac{2^n+6^n-4^{n-1}}{3^n+6^{n+1}}b) limdfrac{1+3+5+...+left(2n+1right)}{3n^2+4}c) limdfrac{1+2+3+...+n}{n^2-3}d) limleft[dfrac{1}{1.2}+dfrac{1}{2.3}+...+dfrac{1}{nleft(n+1right)}right]e) limleft[dfrac{1}{1.3}+dfrac{1}{3.5}+...+dfrac{1}{left(2n-1right)left(2n+1right)}right]
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Tìm giới hạn các dãy số sau
a) \(lim\dfrac{2^n+6^n-4^{n-1}}{3^n+6^{n+1}}\)
b) \(lim\dfrac{1+3+5+...+\left(2n+1\right)}{3n^2+4}\)
c) \(lim\dfrac{1+2+3+...+n}{n^2-3}\)
d) \(lim\left[\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{n\left(n+1\right)}\right]\)
e) \(lim\left[\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{\left(2n-1\right)\left(2n+1\right)}\right]\)
Tính các giới hạn
a) \(lim\dfrac{1+\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2+...+\left(\dfrac{1}{3}\right)^n}{1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^n}\)
\(lim\left(n^3+n\sqrt{n}-5\right)\)
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Tìm giới hạn dãy số sau
\(lim\dfrac{\left(2n-1\right)\left(3n^2+2\right)^3}{-2n^5+4n^3-1}\)
\(lim\left(3.2^{n+1}-5.3^n+7n\right)\)
Tính các giới hạn
a) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+3}{3x-1}\)
b) \(\lim\limits_{x\rightarrow+\infty}\dfrac{\left(\sqrt{x^2+1}+x\right)^n-\left(\sqrt{x^2+1}-x\right)^n}{x}\)
Biết \(\lim\limits_{x\rightarrow1}\left[\dfrac{5}{\left(x-1\right)^2}\left(a+\dfrac{x+1}{\sqrt{x^2-x+1}}-\dfrac{3x+3}{\sqrt{x}}\right)\right]=\dfrac{b}{c}\) là phan số tối giản. Tính a+b+c