Numerical integration is the process of evaluating a definite integral from a set of tabulated values of the integrand. This process when applied to a function of a single variable, is known as quadrature. in this article, we have discussed Newton-Cote's formula and derived the Trapezoidal rule. In the end, we solved a few examples depending on the Trapezoidal rule and gave a few examples to practice.
What is the Newton‑Raphson Method? Derivation of the Algorithm Step-by-Step Example Convergence and Limitations Application in GATE / Engineering Maths Download PDF Notes Newton-Raphson Method: In this article, we discuss the formula of the Newton-Raphson method, its limitations, and its advantages. Also, we provide a few solved examples and a few unsolved questions for practice. We discuss Newton iterative formula and then solve a few questions using these iterative formulae. For practice unsolved questions are also provided. This method is generally used to improve the results obtained by one of the previous methods. This method can be derived from Taylor's series. The formula used as follows: $x_{n+1}= x_n - \frac{f(x_n)}{f'(x_n)}$ NOTE: (1)] This method is useful in cases of large values of $f'(x)$ that is , when the graph of $f(x)$ while crossing the x-axis is nearly vertical. (2)] If $f'(x)$ is zero or nearly zero, the me...
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