Ganitagya Gyanam

MCQ ON THE SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS: MCQ on the solution of algebraic and transcendental equations   are discussed here with answers underlined. You can test your knowledge.  0% Question 1: The Iterative formula for Newton Raphson method is A) `x_{n+1} = x_n - \frac{f(x_n)}{f’(x_n)}` B) `x_{n+1} = \frac{x_n - f(x_n)}{f’(x_n)}` C) `x_{n+1} = \frac{x_n + f(x_n)}{f’(x_n)}` D) None Explanation: `x_{n+1} = x_n - \frac{f(x_n)}{f’(x_n)}`. Question 2: In Newton Raphson method if the `f(x)` is constant then `\ldots` A) `f''(x)=0` B) `f(x)=0` C) `f'(x)=0` D) `f'(x)=C` Explanation: `f'(x)=0` Question 3: The Newton-Raphson method fails if `\ldots` A) `f'(x_0)=0` B) `f''(x_0)=0` C) `f(x_0)=0` D) `f'''(x_0)=0` Explanation: `f'(x_0)=0`. Question 4: The Newton-Raphson me...

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...

The Solution of Algebraic and Transcendental Equations Using the Bisection Method: In this post, we first discuss the Bisection method and then solve a few questions using this method given as: 1. Find the root of the equation e x -4x 2 =0 using the bisection method correct up to three decimal places. 2. Find a root of the equation x 3 -4x-10=0 using the bisection method correct up to three decimal places. 3. Find a root of the equation log x-cos x=0 using the bisection method correct up to three decimal places. 4. Find a root of the equation using the bisection method log x cos x=0 correct up to three decimal places.

The solution of Algebraic Equation using the Bisection method: We define the bisection method and find the root of the equation sinx=1/x using the Bisection Method.

SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS (REGULA-FALSI METHOD) In this post, we discuss the Regula- Falsi method. Also, we solve a few questions and give a few numerical for practice. So that you are able to understand the Regula- Falsi method. As we discuss in our previous post about the definition of Algebraic and Transcendental equations. Also, we discuss the Bisection method. Now, we continue further. REGULA-FALSI METHOD: This method is the oldest method of finding the root of the equation `f(x)=0` and resembles to the bisection method. Here, also we find two initial points `x_0` and `x_1` such that `f(x_0)` and `f(x_1)` are of opposite signs. Thus it indicates that a root lies between `x_0` and `x_1` if `f(x_0) f(x_1) If `f(x_0)` and `f(x_2)` are of opposite signs, then the root lies between `x_0` and `x_2`. So replacing `x_1` by `x_2` in equation (1), we obtain the next iteration `x_3`. The root could lie in between `x_1` and `x_2` and we would obtain `x_3` ...

In this article, we discuss the Solution of Algebraic and Transcendental Equations. Then we provide the definition of algebraic and transcendental equations, discuss the Bisection Method, provide the solved examples, and list questions for practice. We will talk about a couple of numerical methods for the solution of algebraic and transcendental equations. For that, we should recognise what algebraic and transcendental equations are. We consider the equation \[ a_{0}\,x^{n} + a_{1}\,x^{\,n-1} + a_{2}\,x^{\,n-2} + \dots + a_{n}=0 \] or the compact form \(f(x)=0\), where \(n\neq0\). For example, if \(n=1\) it becomes a linear equation; if \(n=3\) it is cubic. Hence the expression is called an algebraic equation. When it contains logarithmic, exponential, or trigonometric terms it is called a transcendental equation, e.g. \[ x\,e^{3x}+2 = 0,\quad x^{2}\tan x + 3 = 0,\quad \ta...