limx-->-1=\(\dfrac{x^2+1}{\left(x^2+x\right)\left(x^3+1\right)}=-\infty\)
vì x→-1→ (x2+x )(x3+1) <0
x→-1→limx→-1(x2+1)=2 >0
kiểm chứng bấm máy tính ^^
\(\lim\limits_{x\rightarrow0^-}\left(\dfrac{1}{x^2}-\dfrac{2}{x^3}\right)\)
\(\lim\limits_{x\rightarrow1^+}\dfrac{\sqrt{x^3-x^2}}{\sqrt{x-1}+1-x}\)
\(\lim\limits_{x\rightarrow1^+}\dfrac{1}{x^3-1}-\dfrac{1}{x-1}\)
\(\lim\limits_{x\rightarrow-\infty}\left(x-\sqrt[3]{1-x^3}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-\sqrt[3]{2x^3+x-1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{4x^2+x+1}-2x\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt[3]{x^3+x^2+1}+\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+x+1}-2\sqrt{x^2-x}+x\right)\)
\(\lim\limits_{x\rightarrow+\infty}x\left(\sqrt{x^2+2x}-2\sqrt{x^2+x}+x\right)\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{2x-\sqrt{3x^2+2}}{5x+\sqrt{x^2+1}}\)
\(\lim\limits_{x\rightarrow+\infty}\sqrt{\dfrac{x^2+1}{2x^4+x^2-3}}\)
\(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{1+x^4+x^6}}{\sqrt{1+x^3+x^4}}\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2-x+1}-x\right)\)
\(\lim\limits_{x\rightarrow-\infty}x\left(\sqrt{4x^2+1}-x\right)\)
\(\lim\limits_{x\rightarrow-\infty}\left(4x^5-3x^3+x+1\right)\)
\(\lim\limits_{x\rightarrow+\infty}\sqrt{x^4-x^3+x^2-x}\)
\(\lim\limits_{x\rightarrow-\infty}\left(x-\sqrt{x^2+x+1}\right)\)
\(\lim\limits_{x\rightarrow\pm\infty}\left(\sqrt{x^2+3x+1}-\sqrt{x^2-x+1}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[3]{8x^3+2x}-2x\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt[4]{16x^4+3x+1}-\sqrt{4x^2+2}\right)\)
\(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+1}+\sqrt{x^2-x}-2x\right)\)
\(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt{4x^2-2}+\sqrt[3]{x^3+1}}{\sqrt{x^2+1}-x}\)
\(\lim\limits_{x\rightarrow-\infty}\dfrac{x\sqrt{x^2+1}+2x+1}{\sqrt[3]{2x^3+x+1}+x}\)
\(\lim\limits_{x\rightarrow-\infty}\dfrac{\sqrt[3]{3x^3+1}-\sqrt{2x^2+x+1}}{\sqrt[4]{4x^4+2}}\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{\left(2x+1\right)^3\left(x+2\right)^4}{\left(3-2x\right)^7}\)
\(\lim\limits_{x\rightarrow+\infty}\dfrac{\sqrt{4x^2-3x+4}-2x}{\sqrt{x^2+x+1}-x}\)
1. \(_{\lim\limits_{x->-1^{ }}}\frac{\sqrt{x^2+3}-2}{x+1}\)
2.
\(_{\lim\limits_{x->-3^+}}\frac{1-x}{\left(3+x^2\right)}\)
Helpp mee
Tìm các giới hạn sau :
a) \(\lim\limits_{x\rightarrow-2}\dfrac{x+5}{x^2+x-3}\)
b) \(\lim\limits_{x\rightarrow3^-}\sqrt{x^2+8x+3}\)
c) \(\lim\limits_{x\rightarrow+\infty}\left(x^3+2x^2\sqrt{x}-1\right)\)
d) \(\lim\limits_{x\rightarrow-1}\dfrac{2x^3-5x-4}{\left(x+1\right)^2}\)
