Put the following statements in order to justify why $\displaystyle{\lim_{n \to \infty} \frac{-7 n}{\sqrt{5 n^2 + 1}} = \frac{ -7 }{ \sqrt{ 5 } } }$.
Statements to choose from: Drag these statements to the right column.
1. $= \displaystyle \frac{\displaystyle \lim_{n \to \infty} -7 }{\displaystyle \lim_{n \to \infty} \sqrt{ 5 + 1/n^2 } }$
2. $= \displaystyle \lim_{n \to \infty} \frac{\displaystyle n \cdot -7 }{\displaystyle \sqrt{n^2} \cdot \sqrt{ 5 + 1/n^2 } }$
3. $= \displaystyle \frac{\displaystyle -7 }{\displaystyle \sqrt{ 5 + 0 } }$
4. $= \displaystyle \frac{\displaystyle \lim_{n \to \infty} -7 }{\displaystyle \sqrt{ \lim_{n \to \infty} \left( 5 \right) + \lim_{n \to \infty} \left( 1/n^2 \right) } }$
5. $= \displaystyle \lim_{n \to \infty} \frac{\displaystyle -7 }{\displaystyle \sqrt{ 5 + 1/n^2 } }$
6. $\displaystyle \lim_{n \to \infty} \frac{-7 n}{\sqrt{5 n^2 + 1}}$
7. $= \displaystyle \frac{\displaystyle -7 }{\displaystyle \sqrt { 5 } }$.
8. $= \displaystyle \lim_{n \to \infty} \frac{\displaystyle -7 n }{\displaystyle \sqrt{n^2\left(5 + 1/n^2 \right)} }$
Your justification: Put the statements in order in this column and press the Submit Answers button.
Statements to choose from: Drag these statements to the right column.
1. $= \displaystyle \frac{\displaystyle \lim_{n \to \infty} -7 }{\displaystyle \lim_{n \to \infty} \sqrt{ 5 + 1/n^2 } }$
2. $= \displaystyle \lim_{n \to \infty} \frac{\displaystyle n \cdot -7 }{\displaystyle \sqrt{n^2} \cdot \sqrt{ 5 + 1/n^2 } }$
3. $= \displaystyle \frac{\displaystyle -7 }{\displaystyle \sqrt{ 5 + 0 } }$
4. $= \displaystyle \frac{\displaystyle \lim_{n \to \infty} -7 }{\displaystyle \sqrt{ \lim_{n \to \infty} \left( 5 \right) + \lim_{n \to \infty} \left( 1/n^2 \right) } }$
5. $= \displaystyle \lim_{n \to \infty} \frac{\displaystyle -7 }{\displaystyle \sqrt{ 5 + 1/n^2 } }$
6. $\displaystyle \lim_{n \to \infty} \frac{-7 n}{\sqrt{5 n^2 + 1}}$
7. $= \displaystyle \frac{\displaystyle -7 }{\displaystyle \sqrt { 5 } }$.
8. $= \displaystyle \lim_{n \to \infty} \frac{\displaystyle -7 n }{\displaystyle \sqrt{n^2\left(5 + 1/n^2 \right)} }$
Your justification: Put the statements in order in this column and press the Submit Answers button.