Question

don't understand this limit problem please help

Answer 1

i dont understand why she did that

Answer 2

divide top and bottom by \(n^2\) so you can more easily see which terms dominate

Answer 3

but if you do that in the bottom for example n^3/n^2 you get n not 1/n

Answer 4

$$\frac{3n^2+2n}{\sqrt{n^3+n^2+1}}\cdot\frac{1/n^2}{1/n^2}=\frac{3n^2+2n}{\sqrt{n^3+n^2+1}}\cdot\frac{1/n^2}{\sqrt{1/n^4}}=\frac{3+2/n}{\sqrt{1/n+1/n^2+1/n^4}}$$ so you can clearly

Answer 5

oh so you square it when there is a square root?

Answer 6

Actually he did that..

Answer 7

Oh sorry, that was someone else you did that..

Answer 8

see that in the limit as \(n\to\infty\), the square root tends to \(0\) while the top tends to \(3\); this tells us the terms 'blow up' as \(n\) grows larger and larger since the denominator gets ever smaller

Answer 9

\[\sqrt{\frac{1}{x^2}} = \frac{1}{x} = \sqrt{\frac{1}{x^2}}\]

Answer 10

*who..

Answer 11

When you take x inside squares, it becomes \(x^2\)..

Answer 12

*square root brackets..

Answer 13

oh okay i see

Answer 14

i have one more question

Answer 15

where did the 8 in this problem come from?

Answer 16

the distance between the vertex and focus (\(-4\)) is equal to the distance between the vertex and directrix

Answer 17

so you are add -4+-4?