You are here

Home » Programs » Faculty and Departments » Browse Classroom Capsules and Notes

Browse Classroom Capsules and Notes

You can filter the list below by selecting a subject category from the drop-down list below, for example by selecting 'One-Variable Calculus'. Then click the 'APPLY' button directly, or select a subcategory to further refine your results.

Displaying 41 - 50 of 225

Inverse Hyperbolic Functions as Areas

Analogy of hyperbolic and trigonometric functions

A Self-Contained Derivation of the Formula \( \frac {d x^r}{dx}=r x^{r-1}\)
Differentiating a power of \(x\) when the power is rational.
Average Values and Linear Functions
If and only if characterizations of linear functions.
An Instant Proof of \(e^\pi > \pi^e\)

This proof is three lines long.

A Note on Integration by Parts

Skirt integration by parts using a method of undetermined coefficients.

Relating Differentiability and Uniform Continuity
F is differentiable at a if and only if the difference quotient is uniformly continuous.
Both a Borrower and a Lender Be

Payments on loans also generate continuous interest type problems.

More Applications of the Mean Value Theorem

Inequalities by applying the mean value theorem to \(\ln x\)

Area of a Parabolic Region

A general formula for that area of a parabola in terms of its parameters

Some Interesting Consequences of a Hyperbolic Inequality
Using Geometry to find the proof.

Pages