Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Understanding One-to-One Functions with the Horizontal Line Test: A Crucial Tool in Math

What does the horizontal line test tell you? If the inverse, f-1, is a function. The horizontal line test is a mathematical tool used to determine if...

John Rhodes
June 21, 2023
Calculus

Understanding Inverse Functions: Reflections over the Line y=x

Inverses are reflected over… y = x Inverses are reflected over the line y=x. This means that if we have a function f(x) and it has an...

John Rhodes
June 21, 2023
Calculus

Understanding the Sign of the Derivative: Key to Analyze Function Behavior – Explained with Examples

If f'(x) is always negative (odd exponent) or always positive (even exponent)… then f is one to one and therefore it has an inverse. If f'(x) is...

John Rhodes
June 21, 2023
Calculus

Mastering the Integration of Sin x: Two Methods for Finding Its Antiderivative

∫sin x dx -cos x + c To integrate sin x dx, we can use integration by parts or the substitution method. Method 1: Integration by Parts...

John Rhodes
June 21, 2023
Calculus

Mastering Integration: Simplifying the Process to Solve ∫cos x dx

∫cos x dx sin x + c To integrate cos x dx: We know that the integral of cosine function is sine function. Therefore, ∫cos x dx...

John Rhodes
June 21, 2023
Calculus

Master the Integration of Secant Squared Function: Step-by-Step Guide with Examples

∫sec^2 x dx tan x + c We can begin by using the fact that the derivative of tan(x) is sec^2(x). Using this derivative and the chain...

John Rhodes
June 21, 2023
Calculus

How to Integrate ∫sec x tan x dx using Substitution: Step-by-Step Guide

∫sec x tan x dx sec x + c To integrate ∫sec x tan x dx, we’ll use a technique called substitution. Here is the step-by-step guide:...

John Rhodes
June 21, 2023
Calculus

How to Find The Derivative of Sin x using the Basic Derivative Formula for Trigonometric Functions

d/dx sin x cos x To find the derivative of sin x, we can use the basic derivative formula for trigonometric functions: d/dx sin x = cos...