math help

[RESmonkey]

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?

Thanks in advance

 

[chuckywang]

The limit is infinity.

 

[RESmonkey]

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

 

[axelfox]

The limit DNE

 

[RESmonkey]

Yes it does, from one side*

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

 

[iamaelephant]

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

 

[chuckywang]

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]

The denominator still becomes zero.

 

[iamaelephant]

Originally posted by: RESmonkey
The denominator still becomes zero.

That's because the limit is infinity.

Here you go

 

[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.

 

[RedArmy]

In Soviet Russia, limit finds you!

 

[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?

 

[RESmonkey]

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]

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]

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]

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]

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.)

 

[moshquerade]

somebody is a maaaaaaath teacher.

so is my brother. :thumbsup: