Math by Tathagata
Answer: The derivative of f(x) defined by f(x) = x2sin(1/x) if x≠0 and 0 if x=0 is equal to 0. That if, if f(x) = $\begin{cases} x^2 \sin \left(\dfrac{1}{x} \right) & \text{ if } x \neq 0 \\ 0 & \text{ if } x=0 \end{cases}$, then $f'(0)=0$. Differentiate x^2sin(1/x) Question: Find $f'(0)$ where f(x) is … Read more
Engineering Mathematics Assignments. This page contains a list of assignments for Engineering Mathematics. Unit I and IV: Differential Calculus & Vector Algebra Q1: Show that the following limits do not exist. Q2: If $y=(ax+b)^m$, then find $y_n$. For this, you study the article nth Derivative. Q3: If $y=e^{m \sin^{-1}x}$, then show that $(1-x^2)y_{n+2} -(2n+1)xy_{n+1}$ $- … Read more
Special functions practice problems. A list of practice problems on Special Functions are given here. Problems on Beta Gamma Functions Q1: For what values of m and n, the integral $\displaystyle \int_0^1 x^{m+1}(1-x)^{n-3}\,dx \quad$ converges. Q2: Find the Value of $B\left(\dfrac{1}{2}, \dfrac{1}{2} \right)\quad$ [Solution] Q3: What are the values of $\Gamma(1)$ and $\Gamma(5)$? Q4: Find … Read more
In this page, the syllabus of Engineering Mathematics I is provided. MIDTERM Syllabus (EM-I-MTH11501): For 20 Marks Differential Calculus (10 Marks): Introduction to limits, continuity, derivatives for functions of one variable, Successive differentiation, Leibnitz’s theorem, Rolle’s theorem, Lagrange’s mean value theoremIntegral Calculus (5 Marks): Review of definite integrals, Reduction formulaeLinear Algebra (5 Marks): Basics of … Read more
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
