Đáp án:
`a, lim \frac{5n³ -3n² +6}{4n² -3n³ +7n}=-5/3`
`b,lim \frac{6n⁴ +2n² -1}{1+5n² -3n⁴}=-2`
`c, lim \frac{4n +2017}{\sqrt{4n²+1}+n}=4/3`
Giải thích các bước giải:
`a, lim \frac{5n³ -3n² +6}{4n² -3n³ +7n}`
`= lim \frac{ 5 -3/n +6/(n³)}{4/n -3 +7/(n²)}`
`= \frac{ 5-0+0}{0-3+0}=-5/3`
Vậy ` lim \frac{5n³ -3n² +6}{4n² -3n³ +7n}=-5/3`
`b, lim \frac{6n⁴ +2n² -1}{1+5n² -3n⁴}`
`= lim \frac{ 6 +2/(n²) - 1/(n⁴)}{ 1/(n⁴) +5/(n²) -3}`
`= \frac{6-0-0}{0+0-3} =-2`
Vậy `lim \frac{6n⁴ +2n² -1}{1+5n² -3n⁴}=-2`
`c, lim \frac{4n +2017}{\sqrt{4n²+1}+n}`
`= lim \frac{ 4 +(2017)/n }{ \sqrt{4+1/(n²)} +1}`
`= \frac{ 4+0}{\sqrt{4+0}+1} = 4/3`
Vậy `lim \frac{4n +2017}{\sqrt{4n²+1}+n}=4/3`
