Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

Understanding the Fundamental Concept of Continuity in Mathematics: Definition and Conditions Explained

Definition of Continuity If1. lim x→c f(x) exists.2. f(c) exists.3. lim x→c f(x) = f(c)then f(x) is continuous at c. In mathematics, continuity is a fundamental concept...

John Rhodes
June 21, 2023
Calculus

How the Intermediate Value Theorem Works to Find Solutions to Equations

Intermediate Value Theorem (IVT) If a function is continuous on an interval [a, b] and k is a value between f(a) and f(b) then there will be...

John Rhodes
June 21, 2023
Calculus

Proving the Existence of Function Roots & Intercepts: A Step-by-Step Guide Using the Intermediate Value Theorem

How To Use the IVT 1. Show that f(x) is continuous on [a, b]2. Show that k is between f(a) and f(b)3. State by the IVT, there...

John Rhodes
June 21, 2023
Calculus

Mastering Calculus Limits: Understanding the Fundamental Limits of 1/x and sin(x)/x

Two Special Limits 1. lim x→ 0 (sinx/x) = 12. lim x→ 0 ([1-cosx]/x) = 0 1. The limit as x approaches infinity of 1/x is equal...

John Rhodes
June 21, 2023
Calculus

Master the Basics: Understanding the Limit Definition of Derivative in Calculus

Limit Definition of Derivative f'(x) = lim h→0 ([f(x+h)-f(x)]/h) The limit definition of derivative is a mathematical expression that defines the derivative of a function at a...

John Rhodes
June 21, 2023
Calculus

Understanding the Limit Definition of Derivatives: A Fundamental Concept in Calculus

Limit Definition of a Derivative at a Point f'(a) = lim x→a ([f(x)-f(a)]/[x-a]) The limit definition of a derivative at a point is a mathematical concept used...

John Rhodes
June 21, 2023
Calculus

The Power Rule in Calculus: Deriving Functions Raised to Any Power

Power Rule for Derivatives If f(x) = x^n, then f'(x) = n*x^(n-1) The power rule is a fundamental rule in calculus that allows us to take the...

John Rhodes
June 21, 2023
Calculus

Master the Product Rule for Differentiation: A Fundamental Tool for Optimization, Physics, and Engineering

Product Rule If h(x) = f(x)g(x), then h'(x) = f'(x)g(x)+g'(x)f(x) The product rule is a differentiation formula used to find the derivative of two or more functions...