tìm : \(n\in N\)để :
a)\(\left(2n+9\right)⋮\left(3n+1\right)\)
b)\(\left(5n+2\right)⋮\left(9-2n\right)\)
K
Khách
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DG
1
AH
Akai Haruma
Giáo viên
12 tháng 2 2022
Lời giải:
\(\lim(-2n^3-5n+9)=\lim n^3(-2-\frac{5}{n^2}+\frac{9}{n^3})\)
Khi \(n\to +\infty\Rightarrow \lim n^3=+\infty ; \lim (-2-\frac{5}{n^2}+\frac{9}{n^3})=-2<0\) nên \(\lim (-2n^3-5n+9)=-\infty \)
b. Tương tự phần a, \(\lim (8n-3n^9+1)=-\infty \)
NV
Nguyễn Việt Lâm
Giáo viên
6 tháng 2 2021
\(a=\lim\dfrac{1}{\sqrt{4n+1}+2\sqrt{n}}=\dfrac{1}{\infty}=0\)
\(b=\lim n\left(\sqrt{1+\dfrac{2}{n}}-\sqrt{1-\dfrac{2}{n}}-1\right)=+\infty.\left(-1\right)=-\infty\)
\(c=\lim4^n\left(\sqrt{\left(\dfrac{9}{16}\right)^n-\left(\dfrac{3}{16}\right)^n}-1\right)=+\infty.\left(-1\right)=-\infty\)
\(d=\lim n^3\left(3+\dfrac{2}{n}+\dfrac{1}{n^2}\right)=+\infty.3=+\infty\)
NV
Nguyễn Việt Lâm
Giáo viên
2 tháng 1 2019
\(lim\left(5n-\sqrt{25n^2-3n+5}\right)=lim\dfrac{25n^2-25n^2+3n-5}{5n+\sqrt{25n^2-3n+5}}\)
\(=lim\dfrac{3n-5}{5n+\sqrt{25n^2-3n+5}}=lim\dfrac{3-\dfrac{5}{n}}{5+\sqrt{25-\dfrac{3}{n}+\dfrac{5}{n^2}}}=\dfrac{3-0}{5+\sqrt{25-0+0}}=\dfrac{3}{10}\)
\(lim\dfrac{4n^5-3n^4-2n^3+7n-9}{-5n\left(3n^2-3n+1\right)\left(5-2n^2\right)}=lim\dfrac{\dfrac{4n^5-3n^4-2n^3+7n-9}{n^5}}{\dfrac{-5n}{n}\dfrac{\left(3n^2-3n+1\right)}{n^2}\dfrac{\left(5-2n^2\right)}{n^2}}\)
\(=lim\dfrac{4-\dfrac{3}{n}-\dfrac{2}{n^2}+\dfrac{7}{n^4}-\dfrac{9}{n^5}}{-5.\left(3-\dfrac{2}{n}+\dfrac{1}{n^2}\right).\left(\dfrac{5}{n^2}-2\right)}=\dfrac{4-0-0+0-0}{-5\left(3-0+0\right).\left(0-2\right)}=\dfrac{2}{15}\)
15 tháng 8 2018
a.\(2n^2-3n+1=2n\times\left(n-1\right)-\left(n-1\right)=\left(2n-1\right)\times\left(n-1\right)\Rightarrow2n-1⋮n-1\)
\(\Rightarrow2\left(n-1\right)+1⋮n-1\Rightarrow1⋮n-1\Rightarrow n-1\inƯ\left(1\right)=\left\{1\right\}\Rightarrow n=2\)
b.Tách tương tự nha
15 tháng 8 2018
\(2n^2-3n+1=\left(2n^2-2n\right)-n+1=2n\left(n-1\right)-n+1\)\(\Rightarrow-n+1⋮n-1\Rightarrow-\left(n-1\right)⋮n-1\)
vậy với mọi x thuộc N đều t/m
b) tương tự nha
NV
Nguyễn Việt Lâm
Giáo viên
11 tháng 2 2020
a/ \(=lim\frac{\left(-\frac{2}{3}\right)^n+1}{-2.\left(-\frac{2}{3}\right)^n+3}=\frac{1}{3}\)
b/ \(=lim\frac{\left(2-\frac{1}{n}\right)\left(1+\frac{1}{n}\right)\left(3+\frac{4}{n}\right)}{\left(\frac{5}{n}-6\right)^3}=\frac{2.1.3}{\left(-6\right)^3}=-\frac{1}{36}\)
c/ \(=lim\frac{5n+3}{\sqrt{n^2+5n+1}+\sqrt{n^2-2}}=\frac{5+\frac{3}{n}}{\sqrt{1+\frac{5}{n}+\frac{1}{n^2}}+\sqrt{1-\frac{2}{n}}}=\frac{5}{1+1}=\frac{5}{2}\)
d/ \(=lim\frac{5.\left(\frac{1}{2}\right)^n-6}{4.\left(\frac{1}{3}\right)^n+1}=\frac{-6}{1}=-6\)
e/ \(=-n^3\left(2+\frac{3}{n}-\frac{5}{n^2}+\frac{2020}{n^3}\right)=-\infty.2=-\infty\)
16 tháng 10 2016
a) 2n + 1 + 12 -2n =13
6-n(ư)13 = -1; 1; -13 ; 13
n = 7; 19
b) tương tự, k làm dc mk sẽ làm tiếp
NV
Nguyễn Việt Lâm
Giáo viên
7 tháng 2 2021
\(a=\lim4^n\left(1-\left(\dfrac{3}{4}\right)^n\right)=+\infty.1=+\infty\)
\(b=\lim\left(4^n+2.2^n+1-4^n\right)=\lim2^n\left(2+\dfrac{1}{2^n}\right)=+\infty.2=+\infty\)
\(c=limn^3\left(\sqrt{\dfrac{2}{n}-\dfrac{3}{n^4}+\dfrac{11}{n^6}}-1\right)=+\infty.\left(-1\right)=-\infty\)
\(d=\lim n\left(\sqrt{2+\dfrac{1}{n^2}}-\sqrt{3-\dfrac{1}{n^2}}\right)=+\infty\left(\sqrt{2}-\sqrt{3}\right)=-\infty\)
\(e=\lim\dfrac{3n\sqrt{n}+1}{\sqrt{n^2+3n\sqrt{n}+1}+n}=\lim\dfrac{3\sqrt{n}+\dfrac{1}{n}}{\sqrt{1+\dfrac{3}{\sqrt{n}}+\dfrac{1}{n^2}}+1}=\dfrac{+\infty}{2}=+\infty\)
\(2n+9⋮3n+1\)
\(\Rightarrow3\left(2n+9\right)⋮3n+1\)
\(\Rightarrow2\left(3n+1\right)+25⋮3n+1\)
\(\Rightarrow25⋮3n+1\)
\(\Rightarrow3n+1\in\left\{5,25,1,-5,-25,-1\right\}\)
\(n\in\left\{8,0\right\}\)
\(5n+2⋮9-2n\)
\(\Rightarrow2\left(5n+2\right)⋮9-2n\)
\(\Rightarrow-5\left(9-2n\right)-41⋮9-2n\)
\(41⋮9-2n\)
\(\Rightarrow9-2n\in\left\{41,-41,1,-1\right\}\)
\(\Rightarrow n\in\left\{-16,25,4,-5\right\}\)