Question

how do you find a limit?

Answer 1

any example questions?

Answer 2

limit as x approaches infinity of 3/x^2

Answer 3

Okay

\[\lim_{x \rightarrow \infty}\frac{ 3 }{ x^2 }\]

Well....when you plug infinity in for x.....what does that bottom number (x²) become? REALLY big? or REALLY small?

Answer 4

really big?

Answer 5

Correct....so let me ask you....3/ A REALLY BIG NUMBER....will it be REALLY big....or REALLY small?

Answer 6

really small?

Answer 7

If you know limit laws, you'd be aware that any constants can be taken out. So we can take out the 3:\[\bf = 3*\lim_{x \rightarrow \infty}\frac{1}{x^2}\]Now what happens to 1/x^2 as x goes to zero? What happens to the denominator? And what does this cause the value of the whole fraction to become as x gets larger and larger?

Answer 8

the fraction gets smaller and smaller as x gets bigger

Answer 9

Exactly, so what value is it approaching as x's keep getting larger?

Answer 10

And as @genius12 is showing....once you know that 1/x² is a REALLLLY small number....and then you can multiply by 3....and still get a REALLLY small number. a.k.a 0

the limit approaches 0

Answer 11

What's 1/x^2 when x = 100, what is it when x = 1000000? What value is the function going to as x's are getting larger?

Answer 12

ohhhh thanks johnweldon1993! :D

Answer 13

lol...

Answer 14

And thanks @genius12

Answer 15

ya np

Answer 16

no problem @BeautyQueen327 :)