John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Mastering The Derivative Of Cot X: Using The Quotient Rule For Trigonometric Identities

derivative of cotx -csc^2x The derivative of cot x can be found using the quotient rule. Let us denote certain trigonometric identities: cosec^2 x = 1/sin^2 x,...

John Rhodes
June 21, 2023
Calculus

Discover How To Find The Derivative Of Arcsin X Using Implicit Differentiation

derivative of sin^-1 1/√(1-x^2) The derivative of sin^-1(x) (also expressed as arcsin x or inverse sine of x) can be found using implicit differentiation. Let y =...

John Rhodes
June 21, 2023
Calculus

Discovering The Derivative Of Arctan (Tan^-1): A Step-By-Step Guide

derivative of tan^-1 1/(1 + x^2) The derivative of arctan (tan^-1) is: d/dx arctan(x) = 1 / (1 + x^2) This can be derived using the formula...

John Rhodes
June 21, 2023
Calculus

Continuity In Mathematics: A Guide To Smooth, Uninterrupted Functions

Definition of Continuity:1) ___________________2) ___________________3) ___________________ 1) f(c) is defined2) lim x->c of f(c) exits3) lim x-> c of f(x) = f(c) 1) Continuity is a property...

John Rhodes
June 21, 2023
Calculus

Proving Root Existence: The Importance Of The Intermediate Value Theorem In Calculus And Real Analysis

Intermediate Value Theorem:1) ___________________2) ___________________3) ___________________ then there exits a number c between a and b for which f(c) = k 1) f(x) is continues on [a,b]2)...

John Rhodes
June 21, 2023
Calculus

Demystifying Derivatives: The Fundamental Concept Of Rate Of Change In Mathematics

Definition of the Derivativef'(x) = ___________________ lim h->0 f(x+h)-f(x) / h The derivative of a function f(x) is defined as the rate of change of the function...

John Rhodes
June 21, 2023
Calculus

Using Symmetric Difference Quotient To Define Derivative – An Alternative Approach

Alternative form of the definition of the derivative lim x->c. f(x)-f(c) / x-c An alternative form of the definition of the derivative is: $$f'(x) = \lim_{h\to 0}...

John Rhodes
June 21, 2023
Calculus

Math Explained: Calculating The Limit Of Sin(Theta)/Theta As Theta Approaches 0.

lim theta->0 sin(theta) / theta = ___________________ 1 The limit as theta approaches 0 of sin(theta) / theta is equal to 1. To see why, we can...