diff --git a/curriculum/khanExercise/exercises/limitsAtInfinityGraphical.html b/curriculum/khanExercise/exercises/limitsAtInfinityGraphical.html new file mode 100644 index 0000000..74d4b32 --- /dev/null +++ b/curriculum/khanExercise/exercises/limitsAtInfinityGraphical.html @@ -0,0 +1,293 @@ + + + + + Approximating Limits at Infinity Graphically + + + +
+
+ + + new Polynomial(0,4) + randRange(0,2) + randRange(1,9) + randRangeExclude(-4,4,[p.coefs[4]]) + randRangeNonZero(-1,1) + randRangeNonZero(-1,1) + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+(C-p.coefs[4])*x*x/(x*x+1) + } + } + ) + + makeXList() + makeYList(-8,8,Xs.length) + makeCoordinates(Xs,Ys) + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10; + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10 + } + } + ) + + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10 + } + } + ) + + (function(x){ + if (x <0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10 + } + } + ) + + (function(A){ + if (A > 0){ + return "infinity" + } + else { + return "-infinity" + } + }) + + + sol(E) + sol(D) + + +
+ +
+
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ + +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( f(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + p.coefs[4] +
+ \displaystyle\lim_{x \to -\infty}f(x): + C +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ + +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( g(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + posSol +
+ \displaystyle\lim_{x \to -\infty}f(x): + negSol +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ + +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( h(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + p.coefs[4] +
+ \displaystyle\lim_{x \to -\infty}f(x): + negSol +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ + +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( k(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + posSol +
+ \displaystyle\lim_{x \to -\infty}f(x): + p.coefs[4] +

+ +
+ + +
+ +

hint

+
+
+ + + + + + + +
+ + +
+ + + + + \ No newline at end of file diff --git a/curriculum/khanExercise/exercises/limitsAtInfinityOracle.html b/curriculum/khanExercise/exercises/limitsAtInfinityOracle.html index 754449e..9f5e575 100644 --- a/curriculum/khanExercise/exercises/limitsAtInfinityOracle.html +++ b/curriculum/khanExercise/exercises/limitsAtInfinityOracle.html @@ -1,35 +1,311 @@ - - + + - Limits at Infinity + Approximating Limits at Infinity Graphically - -
- + + + new Polynomial(0,4) + randRange(0,2) + randRange(1,9) + randRangeExclude(-4,4,[p.coefs[4]]) + randRangeNonZero(-1,1) + randRangeNonZero(-1,1) + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+(C-p.coefs[4])*x*x/(x*x+1) + } + } + ) + + makeXList() + makeYList(-8,8,Xs.length) + makeCoordinates(Xs,Ys) + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10; + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10 + } + } + ) + + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10 + } + } + ) + + (function(x){ + if (x <0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10 + } + } + ) + + (function(A){ + if (A > 0){ + return "infinity" + } + else { + return "-infinity" + } + }) + + + sol(E) + sol(D) + +
-
+
+
+ +

+ Consider the function f(x). Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ +

+

f()= ?
+

+ +
+ - + + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( f(input)); + + } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+
-

+
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + p.coefs[4] +
+ \displaystyle\lim_{x \to -\infty}f(x): + C +

+ +
+ + +
+ +

hint

+
-
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+

+

f()= ?
+

+ +
+ + + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( g(input)); + + } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + posSol +
+ \displaystyle\lim_{x \to -\infty}f(x): + negSol +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ +

+

f()= ?
+

+ +
+ + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( h(input)); + + } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + p.coefs[4] +
+ \displaystyle\lim_{x \to -\infty}f(x): + negSol +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ +

+

f()= ?
+

+ +
+ + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( k(input)); + + } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
-
- +

+ \displaystyle\lim_{x \to +\infty}f(x): + posSol +
+ \displaystyle\lim_{x \to -\infty}f(x): + p.coefs[4] +

+ +
+ + +
+ +

hint

+
+
+ + + + + + +
+ +
+ + + \ No newline at end of file diff --git a/curriculum/khanExercise/exercises/limitsAtInfinityOracleGraphical.html b/curriculum/khanExercise/exercises/limitsAtInfinityOracleGraphical.html new file mode 100644 index 0000000..f121eb7 --- /dev/null +++ b/curriculum/khanExercise/exercises/limitsAtInfinityOracleGraphical.html @@ -0,0 +1,380 @@ + + + + + Approximating Limits at Infinity Graphically + + + +
+
+ + + new Polynomial(0,4) + randRange(0,2) + randRange(1,9) + randRangeExclude(-4,4,[p.coefs[4]]) + randRangeNonZero(-1,1) + randRangeNonZero(-1,1) + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+(C-p.coefs[4])*x*x/(x*x+1) + } + } + ) + + makeXList() + makeYList(-8,8,Xs.length) + makeCoordinates(Xs,Ys) + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10; + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10 + } + } + ) + + (function(x){ + if (x >0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+E*x*x/10 + } + } + ) + + (function(x){ + if (x <0){ + return p.evalOf(x)/(x*x*x*x+A*x*x+B); + } + else { + return p.evalOf(x)/(x*x*x*x+A*x*x+B)+D*x*x/10 + } + } + ) + + (function(A){ + if (A > 0){ + return "infinity" + } + else { + return "-infinity" + } + }) + + + sol(E) + sol(D) + + +
+ +
+
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ +

+

f()= ?
+

+ +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( f(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 2 + }); + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( f(input)); +
+ ellipse( [input,f(input)], 1/4, { + stroke: "none", + fill: GREEN + }); +
+ } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + p.coefs[4] +
+ \displaystyle\lim_{x \to -\infty}f(x): + C +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+

+

f()= ?
+

+ +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( g(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( g(input)); +
+ ellipse( [input,g(input)], 1/4, { + stroke: "none", + fill: GREEN + }); +
+ } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + posSol +
+ \displaystyle\lim_{x \to -\infty}f(x): + negSol +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ +

+

f()= ?
+

+ +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( h(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( h(input)); +
+ ellipse( [input,h(input)], 1/4, { + stroke: "none", + fill: GREEN + }); +
+ } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + p.coefs[4] +
+ \displaystyle\lim_{x \to -\infty}f(x): + negSol +

+ +
+ + +
+ +

hint

+
+
+ +
+ +
+ +

+ Consider the function f(x) graphed below. Find + the value of each of the indicated limits with an error of at most \frac{1}{2}. + If one of the limits appears to be \infty or -\infty, just type "infinity" + or "-infinity". +

+ +

+

f()= ?
+

+ +
+ graphInit({ + range: [20,10], + scale: [12,20], + labelStep: [2,1], + gridOpacity: 0, + axisArrows: "<->" + }); + + plot(function( x ) { + return ( k(x)); + }, [-20, 20], { + stroke: RED, + strokeWidth: 1 + }); + + (function(){ + updateNameDisplay = function() { + var input = parseFloat(this.value) + if (!isNaN(input)){ + $('#nameDisplay').text( k(input)); +
+ ellipse( [input,k(input)], 1/4, { + stroke: "none", + fill: GREEN + }); +
+ } + else {$('#nameDisplay').text("?")}; + }; + $('#nameField').keydown( updateNameDisplay ); + $('#nameField').keyup( updateNameDisplay ); + $('#nameField').keypress( updateNameDisplay ); + })() +
+ +
+ +
+ +

+ \displaystyle\lim_{x \to +\infty}f(x): + posSol +
+ \displaystyle\lim_{x \to -\infty}f(x): + p.coefs[4] +

+ +
+ + +
+ +

hint

+
+
+ + + + + + + +
+ + +
+ + + + + \ No newline at end of file