# Khan/khan-exercises

graphie for limits_1

sophiebits committed Jul 14, 2011
1 parent fc50ea9 commit 3cd4d79070fe2cdf5cfa0822f0384690940cc63c
Showing with 82 additions and 30 deletions.
1. +82 −30 exercises/limits_1.html
 @@ -1,5 +1,5 @@ - + Limits 1 @@ -23,10 +23,24 @@ limtoa -

-
- plot('(' + quadratic + LINE + ')/' + LINE); - ASdot([a, limtoa], 4, "black", "white"); +

+
+ graphInit({ + range: 10, + scale: 20, + tickStep: 1, + axisArrows: "->" + }); + + style({ + stroke: "#6495ed" + }, function() { + plot( function(x) { + return q_lcoef * x * x; + }, [-10, 10] ); + + circle( [a, limtoa], 4 / 20, { fill: "white" } ) + });

limtoa

@@ -55,12 +69,23 @@

-
- line([-11, abs_coef * -1], [-1 * abs_cons, abs_coef * -1]); - line([-1 * abs_cons, abs_coef], [11, abs_coef]); +
+ graphInit({ + range: 10, + scale: 20, + tickStep: 1, + axisArrows: "->" + }); - ASdot([-1 * abs_cons, -1 * abs_coef], 4, "black", "white"); - ASdot([-1 * abs_cons, abs_coef], 4, "black", "white"); + style({ + stroke: "#6495ed" + }, function() { + line( [-11, abs_coef * -1], [-abs_cons, abs_coef * -1] ); + line( [-abs_cons, abs_coef], [11, abs_coef] ); + + circle( [-abs_cons, -abs_coef], 4 / 20, { fill: "white" } ) + circle( [-abs_cons, abs_coef], 4 / 20, { fill: "white" } ) + });

Does not exist.

@@ -75,7 +100,7 @@
• randRangeNonZero(-3, 3)
-

The limit as we approach from the left doesn't match the limit as we approach from the right, so \lim_{x\toa} doesn't exist.

+

The limit as we approach from the left doesn't match the limit as we approach from the right, so f(x) has no limit as x \to a.

@@ -103,10 +128,24 @@ d_cons &\quad \text{if} \quad x = a\\ \end{array} \right. \end{align*}

-
- plot(d_line); - ASdot([a, limtoa], 4, "black", "white"); - ASdot([a, d_cons], 4, "blue", "blue"); +
+ graphInit({ + range: 10, + scale: 20, + tickStep: 1, + axisArrows: "->" + }); + + style({ + stroke: "#6495ed" + }, function() { + plot( function(x) { + return l_coef * x + l_cons; + }, [-10, 10] ); + + circle( [a, limtoa], 4 / 20, { fill: "white" } ) + circle( [a, d_cons], 4 / 20, { fill: "#6495ed", stroke: "none" } ) + });

limtoa

@@ -135,8 +174,21 @@

-
- plot(q_lcoef + 'x^2 + ' + q_cons); +
+ graphInit({ + range: 10, + scale: 20, + tickStep: 1, + axisArrows: "->" + }); + + style({ + stroke: "#6495ed" + }, function() { + plot( function(x) { + return q_lcoef * x * x + q_cons; + }, [-10, 10] ); + });

limtoa

@@ -153,35 +205,35 @@

What happens as we approach x = a from the left?

-
- line([a > 0 ? 0 : a + a, 0], [a, 0]); +
+ line( [a - 2, 0], [a, 0], { + stroke: "#ff00af", + arrows: "->" + });
xa - 0.1a - 0.01a - 0.001
f(x)curFunc(a - 0.1).toFixed(4)curFunc(a - 0.01).toFixed(4)curFunc(a - 0.001).toFixed(4)
- It looks like f(x) is approaching l_limtoa from the left. -
- line([a, 0], [a, l_limtoa]); -
+ It looks like f(x) is approaching l_limtoa from the left.

When we approach x = a from the right, we get:

xa + 0.1a + 0.01a + 0.001
f(x)curFunc(a + 0.1).toFixed(4)curFunc(a + 0.01).toFixed(4)curFunc(a + 0.001).toFixed(4)
- It looks like f(x) is approaching r_limtoa from the right. -
- line([a < 0 ? 0 : a + a, 0], [a, 0]); -
-
- line([a, 0], [a, r_limtoa]); + It looks like f(x) is approaching r_limtoa from the right. +
+ line( [a + 2, 0], [a, 0], { + stroke: "#ff00af", + arrows: "->" + });
-

So \lim_{x\toa} = limtoa

+

So the limit is limtoa.