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About Me

Hello guys! I am Mohan Singh 

Welcome to Mathematical World, your number one source for all things related to Mathematics. I am dedicated to giving you the very best of Mathematics Solutions with a focus on quality and real-world problem solution.

Founded in 2021-03-25 by Mohan Singh, Mathematical World has come a long way from its beginnings in 226202 located in India. When I first started out, my passion for Mathematics drove us to start my own blog/website.

We hope you enjoy my blog as much as I enjoy offering them to you. If you have any questions or comments, please don't hesitate to contact me.

Sincerely, Mohan Singh

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What are Function and how its work on Calculus?

What are Function ? Table Of Contents Introduction with beautiful example Here's a plant, and what you see here is it's  shadow. Can you list the things that the length of the shadow is dependent on. One, it's dependent on the position of the source of light. Anything else that you can think of. If the height of the plant grows then the shadows length will also change, right. So the length of the shadow is dependent on the position of the source of light, and the height of the plant too. So we can say that the length of the shadow is a function of the following two things. The output is dependent on these two things, which could be considered as the inputs. That's a very simple way to understand functions. Could you think of more inputs, this output is dependent on here, tell us yours answers in the comment section below.  How do Function work in calculus ? That's what we'll see in this topics. Previously, we saw an idea to find the instant...
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Method of differntiation - Notes, Concept and All Important Formula

METHODS OF DIFFERENTIATION 1. DERIVATIVE OF f(x) FROM THE FIRST PRINCIPLE : Obtaining the derivative using the definition \(\displaystyle\displaystyle \lim_{\delta x \rightarrow 0} \dfrac{\delta y}{\delta x}= \displaystyle\displaystyle \lim_{\delta x \rightarrow 0} \dfrac{f(x+\delta x)-f(x)}{\delta x}=f^{\prime}(x)=\dfrac{d y}{d x}\) is called calculating derivative using first principle or ab initio or delta method. All Chapter Notes, Concept and Important Formula 2. FUNDAMENTAL THEOREMS : If \(f\) and \(g\) are derivable function of \(x\) , then, (a) \(\dfrac{\mathrm{d}}{\mathrm{dx}}(\mathrm{f} \pm \mathrm{g})=\dfrac{\mathrm{df}}{\mathrm{dx}} \pm \dfrac{\mathrm{d} \mathrm{g}}{\mathrm{d} \mathrm{x}}\) , known as SUM RULE (b) \(\dfrac{\mathrm{d}}{\mathrm{dx}}(\mathrm{cf})=\mathrm{c} \dfrac{\mathrm{df}}{\mathrm{dx}}\) , where \(\mathrm{c}\) is any constant (c) \(\dfrac{\mathrm{d}}{\mathrm{dx}}(\mathrm{fg})=\mathrm{f} \dfrac{\mathrm{dg}}{\mathrm{dx}}+\mathrm{g} \dfrac{\mathrm{df}...
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Hyperbola - Notes, Concept and All Important Formula

HYPERBOLA The Hyperbola is a conic whose eccentricity is greater than unity \((e>1) .\) 1. STANDARD EQUATION & DEFINITION(S): Standard equation of the hyperbola is \(\dfrac{\mathbf{x}^{2}}{\mathbf{a}^{2}}-\dfrac{\mathbf{y}^{2}}{\mathbf{b}^{2}}=\mathbf{1},\) where \(b^{2}=a^{2}\left(e^{2}-1\right)\) or \(a^{2} e^{2}=a^{2}+b^{2}\)    i.e.    \(e^{2}=1+\dfrac{b^{2}}{a^{2}}\) \(=1+\left(\dfrac{\text { Conjugate Axis }}{\text { Transverse Axis }}\right)^{2}\) (a) Foci : \(\mathrm{S} \equiv(\mathrm{a} e, 0) \quad \& \quad \mathrm{~S}^{\prime} \equiv(-\mathrm{a} e, 0) .\) (b) Equations of directrices: \(\mathrm{x}=\dfrac{\mathrm{a}}{e}\quad \) & \(\quad \mathrm{x}=-\dfrac{\mathrm{a}}{e}\) (c) Vertices: \(A \equiv(a, 0)\quad \) & \(\quad A^{\prime} \equiv(-a, 0)\) (d) Latus rectum: (i) Equation: \(\mathrm{x}=\pm \mathrm{ae}\) (ii) Length:  \(\begin{aligned} &=\dfrac{2 b^{2}}{a}=\dfrac{(\text { Conjugate Axis })^{2}}{(\text { Transverse Axis ...
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