John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Exploring The Limit Definition Of Derivative: Finding Instantaneous Rate Of Change

Limit Definition of Derivative limit (as h approaches 0)= F(x+h)-F(x)/h The limit definition of derivative is a mathematical formula used to find the slope of the tangent...

John Rhodes
June 21, 2023
Calculus

The Derivative: The Key To Calculus And Real-Life Problem Solving

Alternate Definition of Derivative limit (as x approaches a number c)=f(x)-f(c)/x-c x≠c In mathematics, the derivative of a function is a measure of how much the function...

John Rhodes
June 21, 2023
Calculus

Discovering The Limit Of Sinx/X: An Application Of L’Hopital’S Rule

limit as x approaches 0: sinx/x 1 To evaluate the limit as x approaches 0 for sinx/x, we need to apply L’Hopital’s rule, as we have an...

John Rhodes
June 21, 2023
Calculus

Evaluating Limits: Algebraic Manipulation And L’Hopital’S Rule For 1-Cosx/X.

limit as x approaches 0: 1-cosx/x 0 To evaluate the given limit, we can either use algebraic manipulation or L’Hopital’s rule. I will show both methods: Algebraic...

John Rhodes
June 21, 2023
Calculus

The Continuity Rule: Simplifying Limit Evaluations In Calculus

Continuity Rule If the limit exists (aka left limit and right limit are equal), and the limit equals the function at that point. The continuity rule pertains...

John Rhodes
June 21, 2023
Calculus

Mastering The Basics: 5 Rules For Finding Derivatives In Calculus

Basic Derivative f(x^n)= nX^(n-1) A derivative is a mathematical concept that represents the instantaneous rate of change of one variable with respect to another. In calculus, the...

John Rhodes
June 21, 2023
Calculus

Explaining The Derivative Of Sin(X) And Its Trigonometric Derivation.

d/dx(sinx) cosx The derivative of sin(x) with respect to x is cos(x). To understand why this is true, we can use the following derivation: Let’s start with...

John Rhodes
June 21, 2023
Calculus

Mastering Derivatives: Step-By-Step Guide To Using Chain Rule In Differentiating Tan(X)

d/dx(tanx) sec²x We will use the chain rule to differentiate the given function. Let y = tan(x) Using the derivative of tan(x), we know that y’ =...