From 0af69d90afc796049827ef1dd55905ca6523fda5 Mon Sep 17 00:00:00 2001 From: APEXCalculus Date: Tue, 23 Jul 2024 21:12:06 -0400 Subject: [PATCH 01/13] Section 1.1-1.4 shifts --- ptx/apex.ptx | 35 +++-------------- ptx/chapter_limits.ptx | 7 ++++ ptx/sec_limit_analytically.ptx | 60 +++++++++++++++--------------- ptx/sec_limit_continuity.ptx | 68 +++++++++++++++++----------------- ptx/sec_limit_def.ptx | 6 +-- ptx/sec_limit_intro.ptx | 15 ++++---- xsl/apex-latex-print-style.xsl | 2 +- 7 files changed, 91 insertions(+), 102 deletions(-) diff --git a/ptx/apex.ptx b/ptx/apex.ptx index ce5bafeb6..08b677742 100644 --- a/ptx/apex.ptx +++ b/ptx/apex.ptx @@ -5,6 +5,7 @@ APEX Calculus + - - - - - - - - - - - - - + - + + Answers to Selected Exercises @@ -101,5 +77,6 @@ + diff --git a/ptx/chapter_limits.ptx b/ptx/chapter_limits.ptx index 1ef208e62..2564dc380 100644 --- a/ptx/chapter_limits.ptx +++ b/ptx/chapter_limits.ptx @@ -21,11 +21,18 @@ + + + + + Chapter Summary diff --git a/ptx/sec_limit_analytically.ptx b/ptx/sec_limit_analytically.ptx index 9d38baf19..e041662ca 100644 --- a/ptx/sec_limit_analytically.ptx +++ b/ptx/sec_limit_analytically.ptx @@ -199,7 +199,7 @@ \amp = 3\bigl(\lim_{x\to 2}x\bigr)^2-5\lim_{x\to 2}(x) +7 \amp = 3\cdot 2^2 - 5\cdot 2+7 \amp = 9 - + .

@@ -345,9 +345,10 @@
  • \lim_{x\to c}\sqrt[n]{x} = \sqrt[n]{c}
    • - ( follows from the +

    @@ -478,7 +479,33 @@ That is what the Squeeze Theorem states. This is illustrated in .

    -
    + + + Squeeze Theorem +

    + Let f, + g and h be functions on an open interval I + containing c such that for all x in I, + + f(x)\leq g(x) \leq h(x) + . + + limitSqueeze Theorem + Squeeze Theorem + + If + + \lim_{x\to c} f(x) = L = \lim_{x\to c} h(x) + , + then + + \lim_{x\to c} g(x) = L + . +

    +     +     + +
    An illustration of the Squeeze Theorem @@ -519,32 +546,7 @@
    - - - Squeeze Theorem -

    - Let f, - g and h be functions on an open interval I - containing c such that for all x in I, - - f(x)\leq g(x) \leq h(x) - . - - limitSqueeze Theorem - Squeeze Theorem - - If - - \lim_{x\to c} f(x) = L = \lim_{x\to c} h(x) - , - then - - \lim_{x\to c} g(x) = L - . -

    -     -     - +
    Explaining the Squeeze Theorem