Question

Calculus help
please can anyone explain to me y the answer to this q?

f(x)=x+2/x^2-3x-10 which the answer is removable discontinuity at x=-2 and nonremovable discontinuity at x=5

Answer 1

can u please help me? :[

Answer 2

the eaquation is undefined at x = -2 and x = 5 but the derevative is undefined at x = 5

Answer 3

we haven't studied derivatives....yet

Answer 4

o, im thinking of a good way to say this

Answer 5

k :]

Answer 6

help anyone?

Answer 7

bump it to the top

Answer 8

can't not yet

Answer 9

plz HELP :[

Answer 10

With a removable discontinuity, the limit will exist (Do you know how to take a limit?) but the value of the function at that point will not approach the limit.

Answer 11

yes i know how to take a limit the second part u said or wrote confused me....the value of the function at that point will not approach the limit???????

Answer 12

In other words, in the case of the removable discontinuity, if you take the limit as it approaches -2, in this example, the limit turns out to be different from the solution if you simply plug -2 into the equation and solve.

Answer 13

i'm so sorry i'm really slow at math can u like dumb it down/? lol if thats possible?

Answer 14

pease?

Answer 15

nevermind i understand wat u were trying 2 say

Answer 16

Ok, sorry. I'm trying to think of how to put this since you don't know derivatives (they make this MUCH easier)

Answer 17

I suggest graphing the equation

Answer 18

But here, if you use the substitution method for taking the limit as x approaches -2, you will find that you get 0/0, with what you know now, the limit does not exist. The key is rewriting the equation to look different so we can see if the limit DOES exist (it actually does exist)

Answer 19

Follow?

Answer 20

yes!

Answer 21

Ok, so the key here is to try to make it so the numerator doesn't evaluate to 0. Can you factor the denominator?

Answer 22

yeah

Answer 23

What do you get now?

Answer 24

x+2/(x-5)(x+2)

Answer 25

Perfect. What happens to the x+2 terms?

Answer 26

they cancel

Answer 27

So you get what?

Answer 28

1/x-5

Answer 29

You got it, now take the limit as x approaches -2. What is it?

Answer 30

-1/7

Answer 31

Right, now go ahead and plug -2 back into the original equation and solve it, what do you get?

Answer 32

0/0

Answer 33

You got it. The limit is saying one thing, but the function does not evaluate there. This is a removable discontinuity. There is a hole in the graph at x = -2

Answer 34

In the case of the "non-removable discontinuity" (aka Essential discontinuity), it simply means the limit does not exist at all.

Answer 35

Here with 1/(x+5) you can see as the limit approaches 5, it does not exist and there's nothing we can do to make it work for us. This is essential discontinuity. There may be a jump, an asymptote, a step, or something.

Answer 36

okay so basically non-removable means that the limit does not exist at all and removable means that the limit does exist?

Answer 37

Removable means that the limit and the value at that point don't agree. Remember, we made the limit at -2 (removable) work for us. But it just didn't agree with the function at that point.

Essential means the limit won't exist, there are several types though. Essentially that's what you have though.

Answer 38

okay thanks sooooooooooooooooooo much!

Answer 39

No prob. Good luck.

Answer 40

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