update work flow
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@@ -384,6 +384,43 @@ get close to $c$ - allows us to gather quickly if a function seems to
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have a limit at $c$, though the precise value of $L$ may be hard to identify.
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##### Example
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This example illustrates the same limit a different way. Sliding the ``x`` value towards ``0`` shows ``f(x) = \sin(x)/x`` approaches a value of ``1``.
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```=html
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<div id="jsxgraph" style="width: 500px; height: 500px;"></div>
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```
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```ojs
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//| echo: false
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//| output: false
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JXG = require("jsxgraph")
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b = JXG.JSXGraph.initBoard('jsxgraph', {
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boundingbox: [-6, 1.2, 6,-1.2], axis:true
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});
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f = function(x) {return Math.sin(x) / x;};
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graph = b.create("functiongraph", [f, -6, 6])
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seg = b.create("line", [[-6,0], [6,0]], {fixed:true});
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X = b.create("glider", [2, 0, seg], {name:"x", size:4});
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P = b.create("point", [function() {return X.X()}, function() {return f(X.X())}], {name:""});
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Q = b.create("point", [0, function() {return P.Y();}], {name:"f(x)"});
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segup = b.create("segment", [P,X], {dash:2});
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segover = b.create("segment", [P, [0, function() {return P.Y()}]], {dash:2});
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txt = b.create('text', [2, 1, function() {
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return "x = " + X.X().toFixed(4) + ", f(x) = " + P.Y().toFixed(4);
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}]);
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```
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##### Example
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@@ -436,8 +473,6 @@ $g(x) = (x-3)/(x+3)$ when $x \neq 2$. The function $g(x)$ is
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$g(2) = (2 - 3)/(2 + 3) = -0.2$ it would be made continuous, hence the
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term removable singularity.
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## Numerical approaches to limits
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The investigation of $\lim_{x \rightarrow 0}(1 + x)^{1/x}$ by
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