Lời giải:
\(\lim\limits_{x\to 5}\frac{2+\sqrt{x-4}-\sqrt{x+4}}{x-5}=\lim\limits_{x\to 5}\frac{(\sqrt{x-4}-1)-(\sqrt{x+4}-3)}{x-5}=\lim\limits_{x\to 5}\frac{\frac{x-5}{\sqrt{x-4}+1}-\frac{x-5}{\sqrt{x+4}+3}}{x-5}\)
\(=\lim\limits_{x\to 5}\left(\frac{1}{\sqrt{x-4}+1}-\frac{1}{\sqrt{x+4}+3}\right)=\frac{1}{3}\)
Câu 1:
a, limx→-∞ \(\dfrac{x+\sqrt{x^2+2}}{\sqrt{8x^2+5x+2}}\)
b, limx→-∞ \(\dfrac{\sqrt{x^2+2x}+3x}{\sqrt{4x^2+1}-x+2}\)
c, limx→-∞ \(\dfrac{x+\sqrt{x^2+x}}{3x-\sqrt{x^2+1}}\)
d, limx→-∞ \(\dfrac{\sqrt{x^2+x+2}+3x}{\sqrt{4x^2+1}-x+1}\)
Câu 1:
a, limx→+∞ (\(\sqrt{x+1}-\sqrt{x}\))
b, limx→+∞ (\(\sqrt{x+\sqrt{x}}-\sqrt{x}\))
c, limx→-∞ (\(\sqrt{3x^2+x+1}+x\sqrt{3}\))
d, limx→+∞ (\(\sqrt{x^2+2x+4}-\sqrt{x^2-2x+4}\))
Tính các giới hạn sau:
Câu 1:
a, limx→\(\pm\)∞ \(\dfrac{\left(2x-3\right)^2\left(4x+7\right)^3}{\left(3x-4\right)^2\left(5x^2-1\right)}\)
b, limx→\(\pm\)∞ \(\dfrac{\sqrt[3]{x^3+2x^2+x}}{2x-2}\)
c, limx→\(\pm\)∞ \(\dfrac{\sqrt[3]{\left(x^3+2x^2\right)^2}+x^3\sqrt{x^3+2x^2}+x^2}{3x^2-2x}\)
d, limx→+∞ \(\dfrac{\left(2-3x\right)^3\left(x+1\right)^2}{1-4x^5}\)
e, limx→+∞ \(\dfrac{\left(2x-3\right)^{20}\left(3x+2\right)^{20}}{\left(2x+1\right)^{50}}\)
g, limx→+∞ \(\dfrac{\left(2x-3\right)^3\left(4x^5+7\right)^9}{11x^{47}-8}\)
limx→-∞
\(\dfrac{1}{4x-2}\sqrt{\dfrac{8x^3+x-1}{x+4}}\)
giúp mình với mn ơi=(((
limx→0\(\dfrac{2\sqrt{1+x}-\sqrt[3]{8-x}}{x}\)
\(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{4x+1}-\sqrt[3]{2x+1}}{x}\)
\(\lim\limits_{x\rightarrow1}\dfrac{\sqrt{4x+5}-3}{\sqrt[3]{5x+3}-2}\)
\(\lim\limits_{x\rightarrow-1}\dfrac{\sqrt[4]{2x+3}+\sqrt[3]{2+3x}}{\sqrt{x+2}-1}\)
cho lim \(\dfrac{f\left(x\right)-5}{x-1}=4\) khi x->1 , lim \(\dfrac{g\left(x\right)-1}{x-1}=5\) khi x->1
tinh lim \(\dfrac{\sqrt{f\left(x\right)\times g\left(x\right)+4}-1}{x-1}\)khi x->1
1/ lim x-> +∞ \(\dfrac{1}{\sqrt{x^2+x+1}-x}\)
2/ lim x->+∞ \(\dfrac{3x-2\sqrt{x}+\sqrt{x^4-5x}}{2x^2+4x-5}\)
help mình vs ạ. cảm ơn ~~~~
1) \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+4x}.\sqrt[3]{1+6x}.\sqrt[4]{1+8x}-1}{x}\)
2)\(\lim\limits_{x\rightarrow1}\dfrac{\sqrt[3]{1+7x}-x^3+3x-4}{x-1}\)
3) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x^3-x^2+1}{2x^2+3x-1}\)
4) \(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{x}+\sqrt[3]{x}+\sqrt[4]{x}}{\sqrt{4x+1}}\)
5) \(\lim\limits_{x\rightarrow-\infty}\dfrac{x+\sqrt{x^2+2}}{\sqrt[3]{8x^3+x^2+1}}\)
6) \(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{4x^2+3x-7}}{\sqrt[3]{27x^3+5x^2+x-4}}\)