Math Questions

Chain Rule in Calculus The Chain Rule in calculus is a fundamental rule for finding the derivative of a composition of two functions. If you have two functions, f(x) and g(x), and you want to find the derivative of their composition, f(g(x)), the chain rule states that: f'(g(x)) = f'(g(x)) × g'(x) Explanation – f(g(x)) […]

What is Derivative in Calculus? In calculus, the derivative measures how a function changes as its input changes. In simpler terms, it represents the rate of change or the slope of the function at any given point. For a function f(x), the derivative f'(x) tells us how fast f(x) is changing at a specific value […]

Mathematical Induction Example Proof statement Problem Statement: Using Mathematical Induction, prove that  for n > 1, the following formula holds true:   Mathematical Proof: First of all, we will prove for the base case n=2. LHS  =    RHS =   Both LHS and RHS ( Left hand side and Right hand side ) are […]

What is Mathematical Induction? Mathematical induction is a method to prove that some statement about the integer n is true for all n. In this method, first, we prove the statement when n has its smallest value, say p0. This is called the base case or basis or trivial case.   Then you prove the […]

Mathematical Induction : Sum of N natural number squares Using Mathematical Induction Prove that the sum of the first n natural number squares is:   i.e Using WolframAlpha to find the formula. WolframAlpha is a great mathematical computational tool for Mathematical students. https://www.wolframalpha.com/       Proof By Mathematical Induction. Base case : P(1) Let’s […]