Approximation methods are techniques used to find solutions to complex problems when exact answers are difficult or impossible to obtain. These methods simplify calculations by using estimates or models that closely represent the original problem, allowing for quicker and more manageable solutions. They are commonly applied in fields like mathematics, physics, and engineering. One popular approximation method is the Taylor series, which expresses functions as infinite sums of terms calculated from the function's derivatives at a single point. Other methods include Monte Carlo simulations and numerical analysis, which help in estimating values and solving equations that cannot be solved analytically.