cho \(lim_{x->1}\dfrac{f\left(x\right)-10}{x-1}=5\)  tính giới hạn \(lim_{x->1}\dfrac{f\left(x\right)-10}{\left(\sqrt{x}-1\right)\left(\sqrt[]{4f\left(x\right)+9}+3\right)}\)  bằng bao nhiêu ?

Tính giới hạn

a, \(Lim_{n->+\infty}\frac{1+sin\left(n\right)+2^{n+2}}{2-2n+2^n}\)

b,\(Lim_{x->0}\frac{e^x-1-xcos\left(x\right)}{x\left(e^{2x}-1\right)}\)

c,\(Lim_{n->+\infty}\sqrt[2n]{8^n+9^n}\)

d,\(Lim_{x->0}\frac{\ln\left(1+x\right)-xe^3}{x\tan\left(2x\right)}\)

Tính giới hạn

a, \(Lim_{n->+\infty}\frac{1+sin\left(n\right)+2^{n+2}}{2-2n+2^n}\)

b,\(Lim_{x->0}\frac{e^x-1-xcos\left(x\right)}{x\left(e^{2x}-1\right)}\)

c,\(Lim_{n->+\infty}\sqrt[2n]{8^n+9^n}\)

d,\(Lim_{x->0}\frac{\ln\left(1+x\right)-xe^3}{x\tan\left(2x\right)}\)

tìm các giới hạn sau

a)\(lim_{x->-\infty}\left(3x+\sqrt{1-2x+9x^2}\right)\)

b)\(lim_{x->+\infty\left(x-\sqrt{1+x+x^2}\right)}\)

\(lim_{x\rightarrow3}\frac{\sqrt{5x+1}-2\sqrt{7x+4}+4\sqrt[3]{x+5}-x+1}{x^2-3x}\)

Tìm các giới hạn sau:

a) \(lim_{x\rightarrow0}\dfrac{tan3x}{sin5x}\)

b) \(lim_{x\rightarrow0}\dfrac{cos2x-1}{sin^23x}\)

c) \(lim_{x\rightarrow1}\dfrac{x^2-4x+3}{sin\left(x-1\right)}\)

Tìm giới hạn hàm số

a)    \(\text{ }lim_{x->3\frac{\sqrt{2x^2-2x-3}-\sqrt{x^2+2x-6}}{x^2-4x+3}}\)

b)\(lim_{x->1\frac{x^3-x^2+2x-2}{x-1}}\)

c)\(lim_{x->1\frac{x^3-x^2+2x-2}{\sqrt{x}-1}}\)

d)\(lim_{x->2\frac{x-\sqrt{x+2}}{\sqrt{4x+1}-3}}\)

\(lim_{x->1}\frac{\sqrt[3]{6x-5}-\sqrt{4x-3}}{\left(x-1\right)^2}\)

l\(lim_{x->0}\left(1-x\right)tan\frac{\pi x}{2}\)