John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 7, 2023
Calculus

Finding the Limit as x Approaches 0 of (1 – cosx)/x: L’Hopital’s Rule vs Trigonometric Identity

limit as x approaches 0: 1-cosx/x To find the limit as x approaches 0 of the expression (1 – cosx)/x, we can use L’Hopital’s rule or apply...

John Rhodes
July 7, 2023
Calculus

Understanding the Limit of sin(x)/x as x Approaches 0: A Trigonometric Approach

limit as x approaches 0: sinx/x To find the limit of sin(x)/x as x approaches 0, we can’t directly substitute 0 into the function because it would...

John Rhodes
July 7, 2023
Calculus

The Alternate Definition of Derivative: A Powerful Tool for Analyzing Discontinuous and Piecewise Functions

Alternate Definition of Derivative In mathematics, the derivative of a function is a fundamental concept that describes how the function changes as its input values change In...

John Rhodes
July 7, 2023
Calculus

Understanding the Limit Definition of Derivative: Exploring the Foundation of Calculus and Instantaneous Rate of Change

Limit Definition of Derivative The limit definition of derivative is a mathematical expression that defines the derivative of a function at a certain point The limit definition...

John Rhodes
July 7, 2023
Calculus

Understanding Decreasing Derivatives: Exploring the Relationship between Tangent Slopes and Rate of Change

If f'(x) is decreasing, then f”(x) is? If the derivative of a function f(x), denoted as f'(x), is decreasing, it means that the slope of the tangent...

John Rhodes
July 7, 2023
Calculus

Understanding the Relationship Between Increasing Derivative and Positive Second Derivative: The Key to Steeper Graph Slopes

If f'(x) is increasing, then f”(x) is? If f'(x) is increasing, it means that as x increases, the derivative f'(x) is becoming larger If f'(x) is increasing,...

John Rhodes
July 7, 2023
Calculus

Understanding Concave Down Functions: The Relationship Between the Second Derivative and Graph Curvature

If f(x) is concave down, then f”(x) is? If a function f(x) is concave down, this means that the graph of the function is curved in a...

John Rhodes
July 7, 2023
Calculus

Understanding Concavity in Calculus: Identifying the Relationship Between the Second Derivative and Graph Shape

If f(x) is concave up, then f”(x) is? If a function f(x) is concave up, it means that its graph is shaped like a U and opens...