Bài Toán giới hạn

[Miu]

Tính giới hạn:
[tex]\lim_{x\rightarrow 0}\frac{e^{2x}-\sqrt{2x+1}}{\sqrt{3x+4}-2-x}[/tex]

[tvhung]

Tính giới hạn:
[tex]\lim_{x\rightarrow 0}\frac{e^{2x}-\sqrt{2x+1}}{\sqrt{3x+4}-2-x}[/tex]

giải giúp Miu:
[tex]A=\lim_{x->o}\frac{e^{2x}-1 -\sqrt{2x+1}+1}{\sqrt{3x+4}-2-x}=\lim_{x->o}\frac{(e^{x}-1)(e^{x}+1)(\sqrt{3x+4}+2+x}{-x(x+1)} - \lim_{x->o}\frac{(\sqrt{2x+1}-1)(\sqrt{2x+1}+1)(\sqrt{3x+4}+2+x)}{-x(x+1)(\sqrt{2x+1}+1)}=0[/tex]

p/s: lưu ý [tex]\lim_{x->o}\frac{e^{x}-1}{x}=1[/tex]

[hoctrofd]

Tính giới hạn:
[tex]\lim_{x\rightarrow 0}\frac{e^{2x}-\sqrt{2x+1}}{\sqrt{3x+4}-2-x}[/tex]

mình giải theo cách này nhé:
[tex]\lim_{x->0}\frac{(e^{4x}-2x-1)(\sqrt{3x+4}+2+x)}{(-x^{2}-x)(e^{2x}+\sqrt{2x+1})}[/tex]
[tex]=\lim_{x->0}\frac{(e^{4x}-1)(\sqrt{3x+4}+2+x)}{4x(\frac{-x}{4}-\frac{1}{4})(e^{2x}+\sqrt{2x+1}}+\lim_{x->0}\frac{(-2x)(\sqrt{3x+4}+2+x)}{x(-x-1)(e^{2x}+\sqrt{2x+1})}[/tex]
[tex]=\lim_{x->0}\frac{(e^{4x}-1)}{4x}.\lim_{x->0}\frac{(\sqrt{3x+4}+2+x)}{(\frac{-x}{4}-\frac{1}{4})(e^{2x}+\sqrt{2x+1})}+\lim_{x->0}\frac{2(\sqrt{3x+4}+2+x)}{(x+1)(e^{2x}+\sqrt{2x+1})}[/tex]
[tex]=1.\lim_{x->0}\frac{(\sqrt{3x+4}+2+x)}{(\frac{-x}{4}-\frac{1}{4})(e^{2x}+\sqrt{2x+1})}+\lim_{x->0}\frac{2(\sqrt{3x+4}+2+x)}{(x+1)(e^{2x}+\sqrt{2x+1})}[/tex]
[tex]=-4[/tex]