Media Summary: In 1872, Karl Weierstrass presented a mathematical "monster"—a function that is Let A(x) = x for x in [-1,1], and extended periodically with period L=2. Then the function f(x):= sum(n=0 to infinity) (2.1/4)^n ... We construct a family of functions depending on two parameters that are
Continuous Everywhere Differentiable Nowhere - Detailed Analysis & Overview
In 1872, Karl Weierstrass presented a mathematical "monster"—a function that is Let A(x) = x for x in [-1,1], and extended periodically with period L=2. Then the function f(x):= sum(n=0 to infinity) (2.1/4)^n ... We construct a family of functions depending on two parameters that are Let A(x) = x for x in [-1,1], and extended periodically with period L=2. Then the function f(x):= sum(n=0 to infinity) (3/4)^n A(4^n x) ... Real Analysis by Prof. S.H. Kulkarni, Department of Mathematics, IIT Madras. For more details on NPTEL visit MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: ...
In this lecture, we have prove that there exist a function which is In this video lecture we will discuss an important result on series of functions "Term by term Differentiation of series of functions". Inequality sin(x) less than or equal to x Inequality cos(x)-cos(y) less than or equal to x-y (Geometric proof + mean value ...
