John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Linear Algebra

Matrix Product Ab And [Ab1 + Ab2 + Ab3]: Showing They Have The Same Entries But Not Always Equal As Matrices

If A and B are 3 x 3 matrices and B = [b1 b2 b3], then AB = [Ab1 + Ab2 + Ab3] False because that expression...

John Rhodes
June 21, 2023
Linear Algebra

Why The Statement The Second Row Of Ab Is The Second Row Of A Multiplied By B Is Not Always True In Matrix Product – An Explanation.

The second row of AB is the second row of A multiplied on the right by B. True because upon multiplying out AB, you will see that...

John Rhodes
June 21, 2023
Calculus

The Limit Definition Of Derivatives And Its Importance In Calculus

Limit Definition of Derivative limit (as h approaches 0)= F(x+h)-F(x)/h The limit definition of the derivative of a function f(x) at a point x=a is given by:...

John Rhodes
June 21, 2023
Calculus

The Difference Quotient: An Alternate Definition Of Derivative In Calculus Mathematics.

Alternate Definition of Derivative limit (as x approaches a number c)=f(x)-f(c)/x-c x≠c An alternate definition of the derivative of a function f(x) is in terms of the...

John Rhodes
June 21, 2023
Calculus

Continuity Rules In Calculus: A Fundamental Concept For Functions

Continuity Rule A function is continuous at x = c if: (1) f(c) is defined (2) lim f(x) (x goes to c) exists (3) lim f(x) (x...

John Rhodes
June 21, 2023
Calculus

Mastering The Chain Rule: Derivatives Of Composite Functions Explained With Example Of F(X)^N

Chain rule of f(x)^n n(f(x)^(n-1))f'(x) The chain rule is a fundamental rule in calculus that allows us to find the derivative of a composite function. If we...

John Rhodes
June 21, 2023
Calculus

The Product Rule In Calculus: How To Find The Derivative Of A Product Of Two Functions

Product rule of f(x)g(x) f'(x)g(x)+g'(x)f(x) The product rule is a fundamental rule in calculus that allows us to find the derivative of a product of two functions....

John Rhodes
June 21, 2023
Algebra

The Absolute Value Function: Definition, Properties, And Applications In Mathematics

absolute value The distance between a real number and zero on a number line. The absolute value of a real number x, denoted by |x|, is defined...