function composition Archives - Infinity is Really Big

September 20, 2019September 26, 2019

The Derivative of y = x^2

Calculus 1, Lectures 4A through 5B

The derivative of x^2 at an arbitrary value of x is 2x. This is the slope of the tangent line at that point. — The derivative of $y=f(x)=x^{2}$ at an arbitrary value of $x$ is equal by $2x$ . This is the slope of the tangent line at that point and is approximated by $2x+\Delta x$ , which are slopes of secant lines.

y=f(x)=x^{2} — The derivative of $y=f(x)=x^{2}$ at an arbitrary value of $x$ is equal by $2x$ . This is the slope of the tangent line at that point and is approximated by $2x+\Delta x$ , which are slopes of secant lines.

Lectures 4A through 5B of my series of Calculus 1 lectures have a lot of content. I will summarize the

… Read the rest

July 12, 2019October 31, 2019

Matrix Multiplication and Composite Transformations

Visual Linear Algebra Online, Section 1.8

The composition of two reflections in the opposite order produces images (blue) that are rotations of each other by $180^{\circ}$ .

180^{\circ} — The composition of two reflections in the opposite order produces images (blue) that are rotations of each other by $180^{\circ}$ .

Function composition is a fundamental binary operation that arises in all areas of mathematics. Function composition is a useful way to create new functions from simpler pieces.

When the functions are linear transformations… Read the rest

March 22, 2019March 25, 2019

De Morgan’s Laws and Commutative Diagrams

New Videos: Videos #3 and #4 on Probability for Actuarial Exam 1/P

As I emphasized in my most recent post “Venn Diagrams and Probability Notation“, simple probability problems are often best solved with pictures and basic logic, but more complicated problems may require formulas.

We are definitely not at the point in my video series where more complicated … Read the rest