What is a Rational number ? Definition and examples
Introduction : Rational number is a fractional number. If an integer is divided by another non zero integer the result we get is either an integer or a fraction for…
what are Natural numbers examples and properties ?
Introduction : Here we shall introduce Natural numbers provide examples and explain their properties. Natural number: A number is a numeric answer to the questions such as how many things,…
Riemann Integrable function solved Question
Introduction : Any function that satisfies conditions of Riemann integral conditions is a Riemann integrable function. An example is solved. Question : Show that following function \[f\left(x\right)=1 , if 2≤x<32\]…
how to find derivative of a power series
Introduction :In this solution, we explain how to find derivative of a power series. Question: Find derivative of a power series \[P^\prime\left(x\right)=1-2\frac{\left(x+2\right)}{6}+\frac{3\left(x+2\right)^2}{27}-\frac{4\left(x+2\right)^3}{108}+\ldots\ldots\] Solution : We have given power series expansion…
Orthogonal and Orthonormal functions Example 1
Introduction: In this example , we will prove that a set of functions is an Orthogonal and Orthonormal functions. Question: Prove that following functions \[f_n (x) = \sqrt {\frac{2}{l}} \sin…
For what values of initial guess x0 does the fixed point iteration sequence converges to the root?
Introduction : In the following question, we apply fixed point theory to determine for what values of initial guess does the fixed point iteration sequence converges to the root as…
What is limit of the sequence 1/n
Introduction : In the following question, we will find the limit of the sequence 1/n by using definition of the limit. Question : Using definition of the limit to prove…
Prove by fixed point theorem that f(x) =exp(-x/2) has a unique fixed point in interval [0, 1]
Introduction : In this solution, we will apply fixed point theorem to prove that f(x)=exp(-x/2) has a unique fixed point in interval [0, 1]. Question : Prove by fixed point…
Mobius Strip Definition and parametrization
Introduction : This post is about learning of Mobius Strip Definition and it's parametrization, we are also plotting graph of mobius strip in matlab. Mobius strip is a mathematical geometrical…