Printable Flashcards

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\begin{center}
  {\large\bfseries\color{accent} Calculus I Flashcards, Set 2: Derivatives}\\[2pt]
  {\small Print single sided, cut along the dashed lines, quiz yourself.}
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\flashcard{0}{0}{Card 1: Definition}
  {State the limit definition of the derivative $f'(a)$.}

\flashcard{1}{0}{Card 2: Product rule}
  {If $h(x) = f(x)\,g(x)$, what is $h'(x)$?}

\flashcard{0}{1}{Card 3: Chain rule}
  {Differentiate $y = \sin\bigl(x^2\bigr)$.}

\flashcard{1}{1}{Card 4: Compute}
  {Find $\dfrac{d}{dx}\Bigl(\dfrac{\ln x}{x}\Bigr)$ for $x > 0$.}

\flashcard{0}{2}{Card 5: Tangent line}
  {Give the tangent line to $y = e^{x}$ at $x = 0$.}

\flashcard{1}{2}{Card 6: Critical points}
  {Find all critical points of $f(x) = x^3 - 3x$ and classify them.}

\flashcard{0}{3}{Card 7: Concept}
  {True or false: if $f$ is differentiable at $a$, then $f$ is continuous
   at $a$. Justify briefly.}

\flashcard{1}{3}{Card 8: L'Hopital}
  {Evaluate $\displaystyle\lim_{x \to 0} \frac{e^{x} - 1 - x}{x^2}$.}

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