# math help

#### RESmonkey

##### Diamond Member
I did Calc A last year, and I'm in BC right now. I forgot a lot of stuff.

Here is the problem:

Lim (1) / ((x+4)^2)
x-> -4 from the left

I can't just plug it in, because the damn denominator becomes a zero. I don't think I'm allowed to use a Calculator. I can't find a way to algebraically simplify that, either.

What am I supposed to do?

#### chuckywang

##### Lifer
The limit is infinity.

#### RESmonkey

##### Diamond Member
How can you find out? Without a calculator, that is.

The limit DNE

#### RESmonkey

##### Diamond Member
Yes it does, from one side*

But how are you guys doing this? (without a calculator)?

#### iamaelephant

##### Diamond Member
Ignore me, I'm too hungover for maths today :

#### chuckywang

##### Lifer
Originally posted by: RESmonkey
How can you find out? Without a calculator, that is.
Informally, "1/0" goes to infinity. The only thing left is to find out if it's positive or negative infinity. Since it's a square on the bottom, it's always positive, so it's positive infinity.

#### RESmonkey

##### Diamond Member
The denominator still becomes zero.

#### invidia

##### Platinum Member
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.

#### RedArmy

##### Platinum Member
In Soviet Russia, limit finds you!

#### Stiganator

##### Platinum Member
Originally posted by: invidia
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.
1/0 is undefined....isn't it?

#### RESmonkey

##### Diamond Member
Originally posted by: invidia
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.
I guess that makes sense. Thanks

#### iamaelephant

##### Diamond Member
Originally posted by: Stiganator
Originally posted by: invidia
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.
1/0 is undefined....isn't it?
Yup, but the function 1/(x+4)^2 is defined everywhere except at the point x=-4, so you can find the value of the function at an infinitesimally small distance from x=-4. The smaller you make that infinitesimally small number, the bigger the function gets, so it can be said to "approach infinity".

#### frostedflakes

##### Diamond Member
Originally posted by: Stiganator
Originally posted by: invidia
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.
1/0 is undefined....isn't it?
Not in calculus.

#### invidia

##### Platinum Member
Originally posted by: Stiganator
Originally posted by: invidia
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.
1/0 is undefined....isn't it?

not in the quantum scale where all laws of classical physics and logic make no sense

#### DrPizza

##### Administrator Elite Member Goat Whisperer
Originally posted by: frostedflakes
Originally posted by: Stiganator
Originally posted by: invidia
just think of it this way. what is 1/(0.0000000000001)? it's some huge number. Now make the denominator even smaller. The name is even bigger. So as you get close to zero in the denominator, you approach infinity.

It's known that 1/0 = infinity. You don't need to show work for that.
1/0 is undefined....isn't it?
Not in calculus.
Actually, in calculus, it IS undefined. You cannot divide by zero. Period. That 0 in the denominator is not actually zero. It *approaches* zero. It's never actually zero. If you were to graph the function in the OP, 0 is not in the domain.

OP: Another easy way to figure out the limit would be to sketch the graph of that function. Unfortunately, though, the two kinda go hand in hand. I spend weeks in pre-calculus teaching students how to sketch rational functions. (Graphing calculators pretty much forbidden during those two weeks.)

##### No Lifer
somebody is a maaaaaaath teacher.

so is my brother. :thumbsup: