Single variable calculus

contents

Interactive worksheets and demos

Average rate of change of a quadratic function. Graphs the secant line through two points and calculates the slope.

Limits 1. Graphs to illustrate \(\lim_{x\to 1}\frac{\left(x^2+x-2\right)}{x-1}\) (in red), \(\lim_{x\to-3}\frac{x}{3x+9}\) (in green), \(\lim_{x\to 0}\frac{\left|x\right|}{x}\) (in purple). secant line through two points and calculates the slope.

Limits 2. More graphs illustrating various limits.

Taylor polynomials for \(y = e^x\), up to degree 6.

Taylor polynomial error. A simpe graph of \(y = \ln x\) and its 3rd degree Taylor polynomial at \(x = 1\), with points on each curve. By sliding the points, you see that they move farther apart as the points move away from \(x = 1\).

Videos

Slope and equation of a line

Chain Rule Example