\(\lim\limits_{x\rightarrow1^+}\dfrac{\sqrt{x^3-x^2}}{\sqrt{x-1}+1-x}\)
\(=\lim\limits_{x\rightarrow1^+}\dfrac{\sqrt{x^2\left(x-1\right)}}{\sqrt{x-1}-\left(x-1\right)}\)
\(=\lim\limits_{x\rightarrow1^+}\dfrac{x}{1-\sqrt{x-1}}=\dfrac{1}{1}=1\)
Cho các số x,y,z thỏa mãn:
\(\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4};2x+3y-z=95\)
Khi đó, x+y+z bằng bao nhiêu?
\(lim\dfrac{2^{n+1}+3n+10}{3n^2-n+2}\)
tính \(\lim\limits_{x\rightarrow+\infty}\) \(\dfrac{\left(x+1\right)\left(x^2+1\right)\left(x^3+1\right)...\left(x^{11}+1\right)}{[\left(11x\right)^{11}+1]^6}\)
\(f\left(n\right)=\left(n^2+n+1\right)^2+1\). Xét dãy \(\left(u_n\right)\) sao cho : \(\left(u_n\right)=\dfrac{f\left(1\right)\cdot f\left(3\right)\cdot f\left(5\right)...\cdot f\left(2n-1\right)}{f\left(2\right)\cdot f\left(4\right)\cdot...\cdot f\left(2n\right)}\). Tính \(\lim\limits_{n\sqrt{u_n}}\)
giá trị của B = lim (2n+3)/(n^2 + 1) =
