0/0
(Redirected from 0÷0)
This page is about the indeterminate form 0/0 - a special case of the division by zero.
The files below show functions r(x), g(x) and their quotients m(x)=r(x)/g(x), c(x)=g(x)/r(x).
Derivatives are drawn in the same color as their function, but thinner.
r(0)/g(0) = r'(0)/g'(0)
[edit | edit source]![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/48/Division_arsinh_x%3B_e%5Ex_-_1.png/425px-Division_arsinh_x%3B_e%5Ex_-_1.png)
f(0)/g(0) = 1
![](http://upload.wikimedia.org/wikipedia/commons/thumb/4/46/Division_sin%28x%29%3B_sinh%28x%29.png/425px-Division_sin%28x%29%3B_sinh%28x%29.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/57/Division_tanh_x%3B_e%5Ex_-_1.png/425px-Division_tanh_x%3B_e%5Ex_-_1.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Division_tanh_x%3B_arsinh_x.png/325px-Division_tanh_x%3B_arsinh_x.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/e9/Division_tanh_x%3B_sinh_x.png/325px-Division_tanh_x%3B_sinh_x.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Division_tanh_x%3B_x.png/325px-Division_tanh_x%3B_x.png)
(coth(x)) / (1/x) |
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![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Division_e%5E%28x%29-1%3B_%28x%2B1%29%5E2-1.png/325px-Division_e%5E%28x%29-1%3B_%28x%2B1%29%5E2-1.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Division_e%5Ex-1%3B_cosh%28x%2Barcosh%282%29%29-2.png/325px-Division_e%5Ex-1%3B_cosh%28x%2Barcosh%282%29%29-2.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/02/Division_e%5E%28x%2B1%29-e%3B_e%5Ex-1.png/425px-Division_e%5E%28x%2B1%29-e%3B_e%5Ex-1.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/2/22/Division_e%5E%28x%2B1%29-e%3B_0%2C5%5E%28x%2B1%29-0%2C5.png/475px-Division_e%5E%28x%2B1%29-e%3B_0%2C5%5E%28x%2B1%29-0%2C5.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Division_2%5E%28x%2B1%29-2%3B_0%2C5%5E%28x%2B1%29-0%2C5.png/425px-Division_2%5E%28x%2B1%29-2%3B_0%2C5%5E%28x%2B1%29-0%2C5.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/62/Division_2%5E%28x%2B1%29-2%3B_0%2C5%5Ex-1.png/425px-Division_2%5E%28x%2B1%29-2%3B_0%2C5%5Ex-1.png)
r'(0) = g'(0) = 0 and r(0)/g(0) = r"(0)/g"(0)
[edit | edit source]r(x) = cosh(x) - 1, g(x) = sinh2(x)
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r(x) = cosh(x) - 1, g(x) = sin2(x)
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r(x) = cos(x)-1, g(x) = x2
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r(x) = cos(x) - 1, g(x) = sinh2(x)
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r(x) = cos(x) - 1, g(x) = sin2(x)
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r(x) = cos(x) - 1, g(x) = cosh(x) - 1
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r(x) = cos(x) - 1, g(x) = cos2(x) - 1
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