Calculus | Senioritis

John Rhodes
July 7, 2023
Calculus

Exploring the Limit of sin(x)/x as x Approaches 0 Using L’Hospital’s Rule and the Limit Definition of the Derivative

lim x->0 sinx/x To find the limit of sin(x)/x as x approaches 0, we can use the concept of L’Hospital’s Rule or the limit definition of the...

John Rhodes
July 7, 2023
Calculus

A Guide to Finding the Limit of sin(bx)/x as x Approaches 0 Using L’Hôpital’s rule

lim x->0 sinbx/x To find the limit of the function sin(bx)/x as x approaches 0, we can use L’Hôpital’s rule To find the limit of the function...

John Rhodes
July 7, 2023
Calculus

Understanding the Derivative at a Point: Exploring Geometric, Physical, and Algebraic Interpretations

What are three different lenses we use to make sense of the derivative at a point f′(. a)? When trying to understand the derivative at a point...

John Rhodes
July 7, 2023
Calculus

Determining the Number and Behavior of Horizontal Asymptotes in Real-Valued Functions

How many horizontal asymptotes can a function have? For a real-valued function, there can be up to two horizontal asymptotes For a real-valued function, there can be...

John Rhodes
July 7, 2023
Calculus

Understanding Vertical Asymptotes: Zero, One, and Multiple Vertical Asymptotes in Functions

How many vertical asymptotes can a function have? A function can have zero, one, or multiple vertical asymptotes A function can have zero, one, or multiple vertical...

John Rhodes
July 7, 2023
Calculus

Evaluating the Limit of f(x)/g(x) when limx→a g(x) = 0: Indeterminate and Non-Indeterminate Cases

If you’re trying to evaluate limx→a f(x)/g(x), and you first find that limx→a g(x) = 0, what else do you need to look at? If you find...

John Rhodes
July 7, 2023
Calculus

Understanding Discontinuities in Functions: Exploring Removable, Jump, and Infinite Discontinuities using Limits

What are the different kinds of discontinuities and how do we describe them using limits? There are three main types of discontinuities in functions: removable, jump, and...

John Rhodes
July 7, 2023
Calculus

Understanding Continuity in Mathematics: Explained with Conditions and Definitions

What does it mean for a function f(x) to be continuous at a point x = a in its domain? When a function f(x) is said to...