John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

Mastering Derivatives: The Alternative Definition Of Derivative For Algebraic Calculations

Alternative form of the definition of the derivative lim x->c. f(x)-f(c) / x-c The derivative of a function f(x) at x=a can be defined alternatively as: lim...

John Rhodes
June 21, 2023
Calculus

Discover The Proof Behind The Limit Of Sin(Theta) / Theta As Theta Approaches 0 = 1 Using Taylor Series Expansion.

lim theta->0 sin(theta) / theta = ___________________ 1 The limit of sin(theta) / theta as theta approaches 0 is equal to 1. To see why this is...

John Rhodes
June 21, 2023
Calculus

Evaluating (1 – Cos(Theta)) / Theta Using Trigonometric Limits And L’Hopital’S Rule

lim theta->0 1 – cos(theta) / theta = ___________________ 0 To evaluate the limit: lim theta->0 1 – cos(theta) / theta We can use L’Hopital’s rule or...

John Rhodes
June 21, 2023
Calculus

Mastering Calculus – The Power Rule For Easy Polynomial Function Derivatives

Power Rule:d/dx [x^n] = ___________________ nx^n-1 The power rule is a rule of differentiation in calculus that states that the derivative of a function of the form...

John Rhodes
June 21, 2023
Calculus

The Derivative Of A Constant Function: Why It’S Always 0

derivative of a constant:d/dx [c] = ___________________ 0 The derivative of a constant c is 0. To understand this, we need to remember that the derivative of...

John Rhodes
June 21, 2023
Calculus

Mastering The Sum And Difference Rules Of Differentiation In Mathematics

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 Importance Of Differentiability In Calculus And Mathematical Analysis

Differentiability implies ___________________ continuity Differentiability implies the existence of a derivative at a point or on an interval. In simpler terms, if a function is differentiable at...

John Rhodes
June 21, 2023
Probability

Unlocking The Genetic Code: Using Probability To Predict Outcomes Of Genetic Crosses

How are the principles of probability used to predict the outcomes of genetic crosses? The principles of probability can be used to predict the outcomes of genetic...