Solving a Single Nonlinear Equation in One Unknown

There are many problems which require the finding of the root of a single nonlinear equation in one unknown. For example, the heat capacity of carbon dioxide is given as a function of temperature as 

7t This defines the nonlinear relationship between heat capacity /, and temperature (Eq. 2.3.2). The format is suitable for the /, bisection and tangent methods  

In general we are seeking the value of the unknown variable, x, which makes the following equation valid 

Often equation (2.3.3) can be rearranged so that the root x appears uniquely as 

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