Calculus Functions
http://www.maa.org/taxonomy/term/40447/0
enDifferentiating the Arctangent Directly
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/differentiating-the-arctangent-directly
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The derivative of arctangent is derived directly from the definition of derivative by using some clever inequalities.</em></p>
</div></div></div>The Utility of Catenaries to Electric Utilities
http://www.maa.org/programs/faculty-and-departments/course-communities/the-utility-of-catenaries-to-electric-utilities
Teaching Tip: How \(\tan x\) Grows
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/teaching-tip-how-tan-x-grows
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>A mysterious pattern when</em> \(\tan x\) <em>tends to infinity is found and explained in terms of L'Hospital's rule.</em></div></div></div>The Derivative of \(\sin \theta\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-derivative-of-sin-theta
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>The author describes a simple way to find the derivative of \(\sin \theta\).</i></p>
</div></div></div>The Differentiability of \(\sin x\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-differentiability-of-sin-x
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Another way to find the derivative of \(\sin x\)</i></p>
</div></div></div>A Discover-\(e\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-discover-e
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>The author uses differentiation to find the point of tangency for exponential functions for all bases and shows they lie on a horizontal line.</i></p>
</div></div></div>Names of Functions: The Problems of Trying for Precision
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/names-of-functions-the-problems-of-trying-for-precision
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Mathematics notation is discussed, focusing on the importance, inconsistencies, eccentricities and abbreviations.</em></div></div></div>Reexamining the Catenary
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/reexamining-the-catenary
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>The author describes a procedure to find the shape of the catenary formed by a chain suspended from two supports with different elevations.</em></div></div></div>Proofs Without Words Under the Magic Curve
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/proofs-without-words-under-the-magic-curve
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The "magic curve" is \(y=1/x\). Various calculus facts are shown by illustration using Riemann sums for the areas of portions of this curve.</em></p>
</div></div></div>A Simple Introduction to \(e\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-simple-introduction-to-e
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Look for a number \(e\) between \(2\) and \(3\) for which the area under \(y=1/x\) from \(1\) to \(e\) is \(1\).</em></div></div></div>Placing Natural Logarithm and Exponential Functions on an Equal Footing
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/placing-natural-logarithm-and-exponential-functions-on-an-equal-footing
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Introduce both the natural log and the exponential as solutions to differential equations</i></p>
</div></div></div>The Spider's Spacewalk Derivation of sin' and cos'
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-spiders-spacewalk-derivation-of-sin-and-cos
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><i>Finds derivatives of trigonometric functions without using limits</i></p>
</div></div></div>Rethinking Rigor in Calculus: The Role of the Mean Value Theorem
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/rethinking-rigor-in-calculus-the-role-of-the-mean-value-theorem
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author proposes the Increasing Function Theorem as an alternative to the Mean Value Theorem in introductory calculus.</em></p>
</div></div></div>Oscillating Sawtooth Functions
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/oscillating-sawtooth-functions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>The author describes examples of sawtooth functions which are derivatives but are not continuous.</em></p>
</div></div></div>Some Interesting Consequences of a Hyperbolic Inequality
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/some-interesting-consequences-of-a-hyperbolic-inequality
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><I>Using Geometry to find the proof.</I></div></div></div>