# 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)

r(x) = arsinh(x), g(x) = ex - 1
f(0)/g(0) = 1

r(x) = sin(x), g(x) = sinh(x)

r(x) = tanh(x), g(x) = ex - 1

r(x) = tanh(x), g(x) = arsinh(x)

r(x) = tanh(x), g(x) = sinh(x)

r(x) = tanh(x), g(x) = x

r(x) = ex - 1, g(x) = (x+1)2 - 1

r(x) = ex - 1, g(x) = cosh(x + arcosh(2)) - 2

r(x) = ex+1 - e, g(x) = ex - 1

r(x) = ex+1 - e, g(x) = 0.5x+1 - 0.5

r(x) = 2x+1 - 2, g(x) = 0.5x+1 - 0.5

r(x) = 2x+1 - 2, g(x) = 0.5x - 1

## r'(0) = g'(0) = 0     and     r(0)/g(0) = r"(0)/g"(0)

### r(x) = cosh(x) - 1, g(x) = sinh2(x)

 Functions and quotients Functions and derivatives

### r(x) = cosh(x) - 1, g(x) = sin2(x)

 Functions and quotients Functions and derivatives

### r(x) = cos(x)-1, g(x) = x2

 Functions and quotients Functions and derivatives

### r(x) = cos(x) - 1, g(x) = sinh2(x)

 Functions and quotients Functions and derivatives

### r(x) = cos(x) - 1, g(x) = sin2(x)

 Functions and quotients Functions and derivatives

### r(x) = cos(x) - 1, g(x) = cosh(x) - 1

 Functions and quotients Functions and derivatives

### r(x) = cos(x) - 1, g(x) = cos2(x) - 1

 Functions and quotients Functions and derivatives