\(\lim\dfrac{1+2.3^{n}-7^{n}}{a+5^{n}+a.7^{n-1}} =\lim\dfrac{(\dfrac{1}{7})^{n}+2.(\dfrac{3}{7})^{n}-1}{a.(\dfrac{1}{7})^{n}+(\dfrac{5}{7})^{n}+\dfrac{a}{7}} =\lim\dfrac{-1}{\dfrac{a}{7}} =\dfrac{-7}{a}\)
1. lim\(\dfrac{\left(n+2\right)^{50}.\left(n-3\right)^{80}}{\left(2n-1\right)^{40}.\left(3n-2\right)^{45}}\)
2. lim\(\dfrac{4^n}{2.3^n+4^n}\)
3. lim\(\dfrac{3^n-2.5^n}{7+3.5^n}\)
4. lim\(\dfrac{4^n-5^n}{2^{2n}+3.5^{2n}}\)
5. lim\(\dfrac{\left(-3\right)^n+5^n}{2.\left(-4\right)^n+5^n}\)
Tìm các giới hạn sau:
a) \(lim\dfrac{5n}{n-\sqrt{n^2-n-1}}\)
b) \(lim\dfrac{\sqrt{n+\sqrt{n+1}}}{n-\sqrt{n}}\)
c) \(lim\dfrac{\sqrt{2n^4-n^2+7}}{3n+5}\)
d) \(lim\dfrac{\sqrt{3n^2+2n}-n}{3n-2}\)
Tính các giới hạn sau:
a) \(\lim\limits\dfrac{\sqrt[3]{n^6-7n^3-5n+8}}{n+12}\)
b) \(\lim\limits\dfrac{1}{\sqrt{3n+2}-\sqrt{2n+1}}\)
c) \(\lim\limits\dfrac{4.3^n+7^{n+1}}{2.5^n+7^n}\)
Tính :6/ lim\(\dfrac{-n^2+2n+1}{\sqrt{3n^4+2}}\)
7/ lim \(\dfrac{\sqrt{n^3-2n+5}}{3+5n}\)
10/ lim\(\dfrac{1+3+5+...+\left(2n+1\right)}{3n^3+4}\)
Tìm các giới hạn sau:
\(a,lim\dfrac{\left(-3\right)^n-4.5^{n+1}}{2.4^n+3.5^n}\)
\(b,lim\dfrac{2^n-3^n+4.5^{n+2}}{2^{n+1}+3^{n+2}+5^{n+1}}\)
Tính các giới hạn :a/ lim \(\dfrac{17n^3+3n^2+4}{2n^3+n}\)
b/ lim \(\dfrac{4^n}{2.3^n+4^n}\)
cho dãy số (un) có \(a=lim\left(1+\dfrac{-1}{2^n}\right)\). tìm gioi hạn \(lim\left(\dfrac{n^5}{n^4-2n^3+1}-an\right)\)
Tìm các giới hạn sau:
\(a,lim\dfrac{\sqrt{2n+1}}{\sqrt{8n}+1}\)
\(b,lim\dfrac{3n+\sqrt{n^2+n-5}}{-2n}\)
Tìm các giới hạn sau:
\(a,lim\dfrac{\sqrt{2n+1}}{\sqrt{8n}+1}\)
\(b,lim\dfrac{3n+\sqrt{n^2+n-5}}{-2n}\)
