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ca.tex

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@@ -408,7 +408,7 @@
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Ji{\v r}\'i Lebl\\[3ex]}
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\today
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\\
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(version 1.0)
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(version 1.1)
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\end{minipage}}
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%\addtolength{\textwidth}{\centeroffset}
@@ -21896,7 +21896,7 @@ \subsection{Differentiation under the integral}
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\end{thm}
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The hypotheses on $f$ and $\frac{\partial f}{\partial y}$ can be
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weakened to some degree, see e.g.\ \exerciseref{exercise:strongerleibniz}.
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weakened to a degree, see e.g.\ \exerciseref{exercise:strongerleibniz}.
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The proof below requires that
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$\frac{\partial f}{\partial y}$ exists and is continuous
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as a function of two variables, and the $x$ interval must be the entire
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\lim_{t \downarrow a} f(t) \quad \Bigl( = \lim_{\substack{t \to a\\t > a}} f(t)
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\Bigr) ,
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\end{equation*}
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as these seemed clearer in some of the situations in this book.
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as these seemed the clearer option in some of the situations in this book.
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We may write $\{ x_n \}$ for a sequence $\{x_n\}_{n=1}^\infty$ and similarly
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$\lim x_n$ instead of $\lim_{n\to \infty} x_n$ when it is clear that $n$ is
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the index of the sequence.

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