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math help

RESmonkey

Diamond Member
May 6, 2007
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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

Lifer
Jan 12, 2004
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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.
 

invidia

Platinum Member
Oct 8, 2006
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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.
 

Stiganator

Platinum Member
Oct 14, 2001
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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
May 6, 2007
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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
Jul 25, 2004
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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
Mar 1, 2005
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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
Oct 8, 2006
2,151
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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
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Mar 5, 2001
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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.)
 

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