Theoretical Issues
https://maa.org/taxonomy/term/40475/all
enAnimating Nested Taylor Polynomials to Approximate a Function
https://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>Some Subtleties in L'HÃ´pital's Rule
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/some-subtleties-in-lh-pitals-rule
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>This is a discusion of the importance of the existence of limits in L'Hôpital's Rule.</p>
</div></div></div>Characterizing Power Functions by Volumes of Revolution
https://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>Average Values and Linear Functions
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/average-values-and-linear-functions
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><I>If and only if characterizations of linear functions.</I></div></div></div>A Simple Auxiliary Function for the Mean Value Theorem
https://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>Relating Differentiability and Uniform Continuity
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/relating-differentiability-and-uniform-continuity
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><I>F is differentiable at a if and only if the difference quotient is uniformly continuous.</I></div></div></div>Self-integrating Polynomials
https://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>More Applications of the Mean Value Theorem
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/more-applications-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><i>Inequalities by applying the mean value theorem to \(\ln x\)</i></p>
</div></div></div>A Generalization of the Mean Value Theorem for Integrals
https://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>Why We Don't Do Calculus on the Rational Numbers
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/why-we-dont-do-calculus-on-the-rational-numbers
<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 shows that The Intermediate Value Theorem, The Maximum Value Theorem, and The Mean Value Theorem all fail for functions continuous on the rationals.</i></p>
</div></div></div>In Praise of \( y = x^{\alpha}\sin(1/x)\)
https://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>A Natural Proof of the Chain Rule
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/a-natural-proof-of-the-chain-rule
<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 gives an elementary proof of the chain rule that avoids a subtle flaw.</i></p>
</div></div></div>Rethinking Rigor in Calculus: The Role of the Mean Value Theorem
https://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>Amortization: An Application of Calculus
https://maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/amortization-an-application-of-calculus
<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 use the Monotonicity Theorem to prove that there is a unique monthly payment that exactly matches the amortization parameters.</em></div></div></div>The Geometric Series in Calculus
https://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>
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