cho \(\lim\limits_{x\rightarrow0}\left(\dfrac{x}{\sqrt[7]{x+1}\sqrt{x+4}-2}\right)=\dfrac{a}{b}\). tìm a,b biết a/b tối giản
Tìm các giới hạn sau :
A=\(\lim\limits_{x\rightarrow0}\frac{\sqrt[3]{x+1}-1}{\sqrt[4]{2x+1}-1}\)
B=\(\lim\limits_{x\rightarrow7}\frac{\sqrt[3]{4x-1}\sqrt{x-2}}{\sqrt[4]{2x+2}-2}\)
C=\(\lim\limits_{x\rightarrow0}\frac{\sqrt{\left(2x+1\right)\left(3x+1\right)\left(4x+1\right)}-1}{x}\)
D=\(\lim\limits_{x\rightarrow0}\frac{\sqrt{1+4x}-\sqrt[3]{1+6x}}{x^2}\)
E=\(\lim\limits_{x\rightarrow0}\frac{\sqrt[m]{1+ax}-\sqrt[n]{1+bx}}{x}\)
Giup mình vớiii
cho \(\lim\limits_{x\rightarrow-\infty}\dfrac{a\sqrt{x^2+1}+2017}{x+2018}=\dfrac{1}{2}\); \(\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+bx+1}-x\right)=2\). Tính P=4a+b
cho f(x) là 1 đa thức thoa man \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-16}{x-1}=24\). tính \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-16}{\left(x-1\right)\left(\sqrt{2f\left(x\right)+4}+6\right)}\)
tìm gioi han \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1.2x+1}.\sqrt[3]{2.3x+1}.\sqrt[4]{3.4x+1}...\sqrt[2018]{2017.2018x+1}}{x}\)
giới hạn \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{x+9}+\sqrt{x+16}-7}{x}=\dfrac{a}{b}\). tìm a,b biết a/b tối giản
biết \(\lim\limits_{x\rightarrow0}\dfrac{\sqrt{3x^2+2}-\sqrt{2-2x}}{x}=\dfrac{a\sqrt{2}}{b}\). tìm a,b biết a/b tối giản
a) lim \(\dfrac{x\sqrt{x^2+1}-2x+1}{^3\sqrt{2x^3-2}+1}\)
x-> -∞
b) lim \(\dfrac{\left(2x+1\right)^3\left(x+2\right)^4}{\left(3-2x\right)^7}\)
x-> -∞
c) lim \(\dfrac{\sqrt{4x^2+x}+^3\sqrt{8x^3+x-1}}{^4\sqrt{x^4+3}}\)
x-> +∞
cho biết \(\lim\limits_{x\rightarrow-\infty}\dfrac{1-\sqrt{4x^2-x+5}}{a\left|x\right|+2}=\dfrac{2}{3}\). tính giá trị a?