John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Learn How To Find Limit Of The Expression As Theta Approaches 0 Using L’Hopital’S Rule

lim theta->0 1 – cos(theta) / theta = ___________________ 0 To find the limit of the given expression as theta approaches 0, we can use L’Hopital’s rule....

John Rhodes
June 21, 2023
Calculus

Master The Fundamentals: The Power Rule In Calculus

Power Rule:d/dx [x^n] = ___________________ nx^n-1 The power rule in calculus states that when we differentiate a function of the form f(x) = xⁿ, where n is...

John Rhodes
June 21, 2023
Calculus

Mastering Derivatives: Why The Derivative Of A Constant Is Always Zero

derivative of a constant:d/dx [c] = ___________________ 0 The derivative of a constant c with respect to x is always zero. Mathematically, it can be expressed as:...

John Rhodes
June 21, 2023
Calculus

Master The Sum And Difference Rule Of Derivatives In Math

Sums and Differences:1) d/dx [f(x) + g(x)] = ___________________2) d/dx [f(x) – g(x)] = ___________________ 1) f'(x) + g'(x)2) f'(x) – g'(x) 1) By applying the sum...

John Rhodes
June 21, 2023
Calculus

The Relationship Between Differentiability And Continuity In Math.

Differentiability implies ___________________ continuity Differentiability implies continuity, but continuity does not necessarily imply differentiability. In more technical terms, if a function f(x) is differentiable at a point...

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...