Question

Giúp mình 3 câu đầu với ạ

Answer 1

1.

\(\lim\left(3-5n-7n^2\right)=\lim n^2\left(\dfrac{3}{n^2}-\dfrac{5}{n}-7\right)\)

Do \(\lim n^2=+\infty\)

\(\lim\left(\dfrac{3}{n^2}-\dfrac{5}{n}-7\right)=0-0-7=-7< 0\)

\(\Rightarrow\lim n^2\left(\dfrac{3}{n^2}-\dfrac{5}{n}-7\right)=-\infty\)

2.

\(\lim\left(3n+8n^2-5\right)=\lim n^2\left(\dfrac{3}{n}+8-\dfrac{5}{n^2}\right)\)

Do \(\lim n^2=+\infty\)

\(\lim\left(\dfrac{3}{n}+8-\dfrac{5}{n^2}\right)=0+8-0=8>0\)

\(\Rightarrow\lim n^2\left(\dfrac{3}{n}+8-\dfrac{5}{n^2}\right)=+\infty\)

3.

\(\lim\left(4-\dfrac{1}{n^5}+\dfrac{7}{n^3}\right)=4-0+0=4\)