Math by Tathagata
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
Uniform Continuity is a special kind of continuity. In this page, we will learn about uniformly continuous functions with examples and related theorems. Notation: I= An interval.ℝ= The set of all real numbers. MOTIVATION: Let f: I → ℝ be a continuous function and c ∈ I. As f is continuous at c, for every … Read more
Continuous functions is an important topic in Real Analysis. On this page, we will study about continuous functions along with its several properties and examples. Definition Definition of a Continuous Function: Let f: D → ℝ be a function and let c ∈ D. We say f is continuous at x=c, if limx→c f(x) = … Read more
The Pigeonhole Principle states that if n containers are occupied by more than n items, then at least one container must contain more than one item. In this page we will study Pigeonhole Principle with its statement and examples. Also, learn about the generalised version of pigeonhole principle. Pigeonhole Principle Statement If n containers are … 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
