Browse Classroom Capsules and Notes

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Animating Nested Taylor Polynomials to Approximate a Function

The authors provide a condition for a function to have nested \(n\)-th degree Taylor polynomials with varying centers, which can approximate the function visually.

Teaching Tip: How \(\tan x\) Grows

A mysterious pattern when \(\tan x\) tends to infinity is found and explained in terms of L'Hospital's rule.

Suspension Bridge Profiles

The author describes the shape of an overhead cable suspended from a horizontal deck with non-uniform lineal mass.

Teaching Tip: Another Way to Break Up Partial Fractions

The author finds a more effective way to deal with partial fractions with an irreducible quadratic denominator.

Teaching Tip: The Limit of \(\frac{\sin t}{t}\)

The authors provide a geometric proof for the limit , \(\frac{\sin t}{t}\), simpler than the geometric proof found in most calculus textbooks.