Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Discovering The Power Of Level Curves In Visualization And Analysis Of Mathematical Functions

level curve of a function of two variables are all of the curves with the equations f(x,y)=k where k is some constant in the range of f...

John Rhodes
June 21, 2023
Calculus

Mastering Function Continuity: A Step-By-Step Guide For Math Enthusiasts

continuity of f(x,y) a function f(x,y) is continuous at (a,b) if limf(x,y)=f(a,b) as (x,y) →(a,b) To determine the continuity of a function f(x,y), we need to check...

John Rhodes
June 21, 2023
Calculus

How And Why Limits Of Math Functions Fail To Exist: Oscillations, Asymptotes, Discontinuity, And Multiple Paths

limit of f(x,y) does not exist if the function does not approach the same limit from every path When the limit of a function f(x,y) does not...

John Rhodes
June 21, 2023
Calculus

Mastering Partial Derivatives: A Comprehensive Guide For Calculus Enthusiasts

definition of a partial derivative fx(x,y)=[f(x+h, y)-f(x,y)]/h A partial derivative is a mathematical concept used in calculus to describe how much a function changes when only one...

John Rhodes
June 21, 2023
Calculus

Mastering The Rules Of Partial Differentiation For Calculus, Physics, And Engineering

rules of partial differentiation to find fx, regard y as a constant and differential f(x,y) with respect to x Partial differentiation is a process of finding the...

John Rhodes
June 21, 2023
Calculus

Clairaut’S Theorem: Importance In Mathematics And Physics

Clairaut’s Theorem of Partial Derivatives suppose that f is defined on a disc D that contains the point (a,b). If both fxy and fyx are continuous, then...

John Rhodes
June 21, 2023
Calculus

Mastering Tangent Planes: Essential Calculus And Differential Geometry Concept

Tangent Plane if f(x,y) has continuous partial derivatives, the equation to the tangent plane to the surface z=f(x,y) at p₀ is: z-z₀=fx(x₀,y₀)(x-x₀)+fy(x₀,y₀)(y-y₀) The tangent plane is defined...

John Rhodes
June 21, 2023
Calculus

Mastering The Art Of Linear Approximation: A Fundamental Technique For Calculus And Engineering Applications

linear approximation f(x,y)≈f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b) Linear approximation is a way to approximate the value of a function near a specific point by using a line tangent to the function...