Theoretical Issues
http://www.maa.org/taxonomy/term/40475/0
enAnimating Nested Taylor Polynomials to Approximate a Function
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/animating-nested-taylor-polynomials-to-approximate-a-function
<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 authors provide a condition for a function to have nested \(n\)-th degree Taylor polynomials with varying centers, which can approximate the function visually.</em></p>
</div></div></div>Investigating Possible Boundaries Between Convergence and Divergence
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/investigating-possible-boundaries-between-convergence-and-divergence
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>Once students master the Integral Test, it is useful to show that there cannot be a series on the boundary between convergence and divergence.</em></div></div></div>On the Indeterminate Form \(0^0\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-the-indeterminate-form-00
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><em>This article gives an explanation of why most textbook examples of the form \(0^0\) have a limit of 1.</em></div></div></div>Off on a Tangent
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/off-on-a-tangent
<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 authors investigate families of curves whose tangent lines at a fixed \(y\)-coordinate go through the origin.</em></div></div></div>Characterizing Power Functions by Volumes of Revolution
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/characterizing-power-functions-by-volumes-of-revolution
<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 authors characterize power functions by ratios of two specific volumes.</em></div></div></div>A Simple Auxiliary Function for the Mean Value Theorem
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-simple-auxiliary-function-for-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"><I>An easier and more intuitive proof of the Mean Value Theorem from Rolle's Theorem.</I></div></div></div>Self-integrating Polynomials
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/self-integrating-polynomials
<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>Student error leads author to seek polynomials for which \(p(1)-p(0)\) equals the integral of \(p(x)\) on \([0,1]\).</em></p>
</div></div></div>A Generalization of the Mean Value Theorem for Integrals
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-generalization-of-the-mean-value-theorem-for-integrals
<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>Links mean value theorem with approximating sums for integrals</i></p>
</div></div></div>In Praise of \( y = x^{\alpha}\sin(1/x)\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/in-praise-of-y-xalphasin1x
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><i>The article discusses a class of counterexamples in analysis.</i></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>The Geometric Series in Calculus
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-geometric-series-in-calculus
<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 argues that many topics in differential and integral calculus could be better approached by an appropriate use of geometric series.</em></p>
</div></div></div>The Importance of Being Continuous
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-importance-of-being-continuous
<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 discusses issues connected with determining a continuous antiderivative for an integrand continuous over a given interval. The solutions obtained by computer algebra systems often do not fulfill this continuity requirement.</em></p>
</div></div></div>Two Methods for Approximating \(\pi\)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/two-methods-for-approximating-pi
<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 summarizes a variety of ways to approximate \(\pi\).</em></p>
</div></div></div>On Antiderivatives of the Zero Function
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/on-antiderivatives-of-the-zero-function
<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 discusses an intuitive direct proof of the fact that functions with zero derivative must be constant, which turns into a rigorous proof by simply invoking the completeness of the real numbers.</em></div></div></div>Arc Length and Pythagorean Triples
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/arc-length-and-pythagorean-triples
<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 family of curves whose lengths are closely related to Pythagorean Triples and therefore rational</em></div></div></div>