# Browse Classroom Capsules and Notes

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Displaying 31 - 40 of 225

Elementary methods for bounding definite integrals

Uses geometry and integration to relate hyperbolic and exponential functions

Alternative method for integration of products of sines and cosines

Various methods are given for evaluating $\lim_{x \rightarrow 0} \frac{\sin x}{x}$.
Solution is obtained for a rectangle in general position inside a triangle.

Obtains optimal solids under various constraints and specified cross-sections

Three classical problems are solved and generalized.

The author obtains a power rule for derivatives of powers with variable exponents.

Systematic use of brackets and parentheses to illustrate rules for calculating derivatives

The midpoint rule is better than the trapazoidal rule for concave functions. A proof without words.