Question

please help step by step.. will fan & medal..

Find the limit of the function algebraically.

limit as x approaches zero of quantity x squared plus two x divided by x to the fourth power.

Answer 1

\[\lim_{x \rightarrow 0} \frac{ x ^{2} + 2x }{ x ^{4}}\]

Answer 2

HI!

Answer 3

hello!

Answer 4

factor and cancel first

Answer 5

you get \[\lim_{x\to 0}\frac{x+2}{x^3}\]

Answer 6

then numerator goes to 2, the denominator goes to zero, so no limit

Answer 7

how does the numerator go to 2 and the demoninator go to zero?

Answer 8

i will let you figure that out for yourself, since it is self evident
replace x by zero

Answer 9

i see it. can u show me how you factored this?

Answer 10

when you get 0 on the denominator by using direct substitution then first you should try to simplify the function. if you still get 0 after simplifying, that means limits doesn't exist but you still need t0 find limit from right and left when x approaches 2 to prove why limit does not exist

Answer 11

\(\color{blue}{\text{Originally Posted by}}\) @lxoser
i see it. can u show me how you factored this?
\(\color{blue}{\text{End of Quote}}\)
\[\huge\rm \frac{ x^2+2x} { x^4 }\] factor the numerator there is x common so take out x from both terms
x^2+2x =x(x+2) and then simplify

Answer 12

Have you learned Lhop rule yet? And differentiation?

Answer 13

i havent..

Answer 14

Okay yes your going to have to factor and stuff than but first always Subsitituite you could get a quick answer from doing that in this case it doesn't work you will get 0/0 so you will have to factor

Answer 15

So what can you fActor out from the top?

Answer 16

What's something they both have in the top?

Answer 17

x^2 + 2x = x(x+2)

Answer 18

Yes and than you can cancel another x from the bottom so what you have left is?

Answer 19

PS please write limit through each steps otherwise you could lose points

Answer 20

You okay?

Answer 21

x + 2 / x^3

Answer 22

Yes now substitiute 0 for x because x is approaching 0