Beta and Gamma Functions: Questions and Answers

Beta Function: The beta function B(m,n) = $\int_0^1$ xm-1(1-x)n-1 dx converges when m,n >0. Gamma Function: The gamma function Γ(n) = $\int_0^\infty$ e-xxn-1dx converges when n >0. Properties of Beta and Gamma Functions: The list of the properties of beta and gamma functions is given below: P1: B(m,n) = B(n,m) P2: B(m,n) = 2$\int_0^{\pi/2}$ sin2m-1θ … Read more

Rolle’s Theorem Questions and Answers

In this post, we will learn about Rolle’s theorem along with examples. We will also discuss some of the related questions of Rolle’s theorem with answers. Rolle’s Theorem Statement Let f(x) be a real-valued function defined on [a, b]. If then there exists at least one element c in (a, b) such that $f'(c)=0$. Examples … Read more