Math by Tathagata
Answer: The Fourier series of x in (-π, π) is given as follows: f(x) = x = $\sum_{n=1}^{\infty} \frac{2}{n} (-1)^{n+1} \sin(nx)$. Fourier Series of x Question: Find the Fourier series of x in the interval (-π, π). Answer: We know that the Fourier series of a function ( f(x) ) in the interval (-π, π) … Read more
Answer: The area of the surface generated by revolving the parabola y2=2ax about x-axis bounded by x=a is equal to 2πa2(3√3-1)/3 unit. In this page, we study the surface area generated by revolving a curve (parabola) about x-axis with formula. The formulas for the volume are given below: Formula • The formula for the area A … Read more
Answer: The volume generated by revolving the parabola y2=2ax about y-axis is equal to (2√2πa3)/5 unit. In this page, we study the volume generated by revolving a curve (parabola) about y-axis with formula. The formulas for the volume are given below: Formula • The formula for the volume V generated by revolving a curve y=f(x) from … Read more
In Complex Analysis, zeroes are points where the function vanishes while singularities are points where the function loses its analytic property (differentiability). Here we study zeros and singularities along with their types, examples, residues and related theorems. Zero of a Function Definition: Let f(z): D → ℂ be a function. A point z=a is called … Read more
The sequences (-1)n and (-1)n/n are special type of sequences. In this page, we will study the convergence of the sequences (-1)^n and (-1)^n/n. Convergence of (-1)n Question: Discuss the convergence of the sequence {(-1)n}. Answer: The sequence {(-1)n} can be written as follows: {(-1)n} = {-1, 1, -1, 1, -1, 1, …}. Therefore, the … Read more
An orthogonal trajectory is a curve that intersects another family of curves at right angles. In this post, we study orthogonal trajectory along with a few questions and answers. Definition of Orthogonal Trajectory An orthogonal trajectory of a family of curves is a curve that intersects every member of that family at a right angle. … Read more
Here, you can find a list of engineering mathematics questions that can be treated as practice problems in Mid-Sem exam, Sep-Oct 2026. Engineering Mathematics I Mid Term Practice Problems 2026 Q1: Find the following limits: Q2: Find the value of k for which the function f(x) = $\begin{cases} \dfrac{1-\cos 4x}{8x^2} \,\, \text{ if } x … Read more
The general form of linear differential equation of first order is of the form: dy/dx + P(x)y = Q(x) where P(x) and Q(x) are functions of x. Using integrating factor method, we solve this equation. In this article, let us learn how to solve a first order linear differential equation with examples. Integrating Factor of … Read more
A series of the form a0+a1x+a2x2+… = ∑ anxn is called a power series. The radius of convergence of a power series is a very powerful tool in many areas of Mathematics. In this article, we will study the convergence of a power series. Definition of Power Series A series of the form a0+a1(x-a)+a2(x-a)2+… = … Read more
A series ∑an is called absolutely convergent if ∑|an| converges. A series ∑an is called conditionally convergent if it converges but not absolutely. In this article, we study absolute and conditional convergence with their definitions and examples. Absolutely Convergent Series Definition: A series $\displaystyle \sum_{n=1}^\infty a_n$ is called absolutely convergent if the series $\displaystyle \sum_{n=1}^\infty … Read more