John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Discovering the Limit of 1 – cos(x) / x as x Approaches 0 Using L’Hopital’s Rule

limit as x approaches 0: 1-cosx/x 0 To find the limit of the expression as x approaches 0, we can attempt to evaluate the expression directly. However,...

John Rhodes
June 21, 2023
Calculus

Mastering the Continuity Rule: Ensuring Smooth Behaviors and Consistent Equations in Mathematics.

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 is...

John Rhodes
June 21, 2023
Calculus

Mastering the Basics of Calculus: Understanding the Derivative Formula for Instantaneous Rate of Change

Basic Derivative f(x^n)= nX^(n-1) The derivative is a mathematical concept used in calculus to represent the instantaneous rate of change of a function with respect to one...

John Rhodes
June 21, 2023
Calculus

Learn how to Calculate the Derivative of sin x with Expert Tips.

d/dx(sinx) cosx To find the derivative of sin x with respect to x, we can use the derivative formula for the sine function, which is: d/dx(sin x)...

John Rhodes
June 21, 2023
Calculus

How to Find the Derivative of Cos(x) Using the Chain Rule: Step-by-Step Guide

d/dx(cosx) sinx To find the derivative of cos(x) with respect to x, we can use the chain rule. The chain rule states that if we have a...

John Rhodes
June 21, 2023
Calculus

Mastering Derivative of Tangent Function: The Quotient Rule Made Easy

d/dx(tanx) sec²x To find the derivative of tangent function, we use the quotient rule. Recall that: (d/dx)(f(x)/g(x)) = [g(x)(d/dx)(f(x)) – f(x)(d/dx)(g(x))]/[g(x)]^2 In this case, we have: f(x)...

John Rhodes
June 21, 2023
Calculus

How to Find the Derivative of Cot(x) using the Quotient Rule: A Comprehensive Guide

d/dx(cotx) csc²x We can find the derivative of cot(x) using the quotient rule. Recall that cot(x) = cos(x)/sin(x). Applying the quotient rule, we have: d/dx(cot(x)) = [sin(x)d/dx(cos(x))...

John Rhodes
June 21, 2023
Geometry

How to Calculate the Area of the Base of 3D Objects: Formulas for Cylinders, Cubes, and Pyramids

area of the base the area of a two dimensional figure that the surface of a solid object stands/sits on The area of the base is the...