Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

The Instantaneous Rate Of Change: An Alternate Definition Of Derivatives

Alternate Definition of Derivative limit (as x approaches a number c)=f(x)-f(c)/x-c x≠c The alternate definition of derivative of a function is the rate of change of the...

John Rhodes
June 21, 2023
Calculus

Evaluating The Limit Of Sin(X)/X As X Approaches 0 Using The Squeeze Theorem

limit as x approaches 0: sinx/x 1 To evaluate the limit as x approaches 0 of sin(x)/x, we can use the squeeze theorem. First, we know that...

John Rhodes
June 21, 2023
Calculus

Mastering Limits: Evaluating (1-Cosx)/X Using L’Hopital’S Rule

limit as x approaches 0: 1-cosx/x 0 To evaluate the limit as x approaches 0 of (1-cosx)/x, we can use L’Hopital’s rule, which states that if we...

John Rhodes
June 21, 2023
Calculus

Analyzing Function Continuity: Applying The Fundamental Continuity Rule 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 is...

John Rhodes
June 21, 2023
Calculus

Unlocking The Power Of Derivatives: And Applying The Mathematical Function’S Measure Of Change

Basic Derivative f(x^n)= nX^(n-1) The derivative of a function is a measure of how the function changes as its input (independent variable) changes. Specifically, the derivative of...

John Rhodes
June 21, 2023
Calculus

Learn How To Find The Derivative Of Sin(X) Using The Chain Rule Of Calculus

d/dx(sinx) cosx The derivative of sin(x) with respect to x can be found using the chain rule of calculus. The chain rule states that if y =...

John Rhodes
June 21, 2023
Calculus

Mastering Calculus: How To Find The Derivative Of Tanx With Secant Squared X

d/dx(tanx) sec²x To find d/dx(tanx), we can use the formula: d/dx(tanx) = sec^2x where sec^2x represents the squared secant of x. So, the derivative of tanx with...

John Rhodes
June 21, 2023
Calculus

Proving Function Continuity Using Limits: A Step-By-Step Guide

f is continuous at x=a f(a) exists, lim x->a f(x) exists, lim x->a f(x) = f(a) To show that a function f is continuous at x=a, we...