Question

Find the limit of 1 / (x - 7)^2 as x approaches 7.

Answer 1

\[\lim_{x \rightarrow 7}\frac{ 1 }{ (x-7)^{2} }\]

Answer 2

yes, I have already done direct substitution and gotten 0. But i'm not sure what to do from here.

Answer 3

sorry i'm lagging badly

Answer 4

\[\frac{1}{0}\neq 0\]

Answer 5

try a number very close to 7 to get a sense of the behavior of that function

Answer 6

I don't understand, if 1/0 does not equal 0, then is there no limit? @satellite73
And I used a graphing calculator and it shows that the function has a horizontal asymptote at y = 0.

Answer 7

\[\frac{ 1 }{ (6.9-7)^{2} } = ? \]

\[\frac{ 1 }{ (6.99-7) ^{2}} = ? \]

\[\frac{ 1 }{ (6.999-7)^{2} }\]

Answer 8

right

Answer 9

that's not necessarily the case

Answer 10

if you you get \[\frac{0}{0}\] then you have more work to do
but if you get \[\frac{a}{0}\] for some non zero \(a\) then forget it

Answer 11

@Photon336
100
10000
1000000

Answer 12

what is that approaching?

Answer 13

what do you notice about that behavior @andrea6201 ?

Answer 14

Positive infinity?

Answer 15

yes

Answer 16

it's not the most fool proof method, but sometimes you can try to pick a number close to where the limit is approaching

Answer 17

Ok so, to be clear, if I get #/0, the limit is non-existent or in other words heading towards infinity?

Answer 18

yes

Answer 19

or negative infinity, or both depending on the direction

Answer 20

satellite would know better.

Answer 21

not hardly

Answer 22

Awesome thank you! How do I give more medals? I want to reward both of you @satellite73 @Photon336

Answer 23

yeah, I know some basic stuff when it comes to this. sometimes you can't always simplify the limit..

Answer 24

no problem @andrea6201

Answer 25

in this case..good to find \[\large\rm \lim_{x \rightarrow 7^{+}} ~~and \lim_{x \rightarrow 7^{-}}\]

Answer 26

Thank you for your input!

Answer 27

yw

Answer 28

yes, nnesha!

\(\lim\limits_{x \rightarrow 7}\frac{ 1 }{ (x-7)^{2} }\)

....it's squared so it's coming in on both sides

so limit does actually exist

the point of it, i guess

Answer 29

o^_^o