| … | |
… | |
| 38 | # Let students type "EmptySet" instead of "NONE" |
38 | # Let students type "EmptySet" instead of "NONE" |
| 39 | Context()->constants->add(EmptySet => Set()); |
39 | Context()->constants->add(EmptySet => Set()); |
| 40 | Context()->flags->set(noneWord=>"EmptySet"); |
40 | Context()->flags->set(noneWord=>"EmptySet"); |
| 41 | |
41 | |
| 42 | $a = random(1,5); |
42 | $a = random(1,5); |
|
|
43 | $a2 = 2*$a; |
| 43 | |
44 | |
| 44 | $ans0 = Compute("$a"); |
45 | $ans0 = Compute("$a"); |
| 45 | $ans1 = Compute("-(1/(2*$a))*(x-$a)^2"); |
46 | $ans1 = Compute("-(1/(2*$a))*(x-$a)^2"); |
| 46 | $ans2 = Compute("-(1/(8*$a^3))*(x-$a)^4"); |
47 | $ans2 = Compute("-(1/(8*$a^3))*(x-$a)^4"); |
| 47 | $ans3 = Compute("-(1/(32*$a^5))*(x-$a)^6"); |
48 | $ans3 = Compute("-(1/(16*$a^5))*(x-$a)^6"); |
| 48 | $ans4 = Compute("-(1/(128*$a^7))*(x-$a)^8"); |
49 | $ans4 = Compute("-(1/(128*$a^6))*(x-$a)^8"); |
| 49 | |
50 | |
| 50 | Context("Numeric"); |
51 | Context("Numeric"); |
| 51 | $ans5 = Compute("$a"); |
52 | $ans5 = Compute("$a"); |
| 52 | ##################################################################### |
53 | ##################################################################### |
| 53 | |
54 | |
| … | |
… | |
| 56 | Find the first five non-zero terms of Taylor series centered at \(x = $a\) for the function below. |
57 | Find the first five non-zero terms of Taylor series centered at \(x = $a\) for the function below. |
| 57 | \[ |
58 | \[ |
| 58 | f(x) = \sqrt{$a2 x - x^2} |
59 | f(x) = \sqrt{$a2 x - x^2} |
| 59 | \] |
60 | \] |
| 60 | $HR |
61 | $HR |
| 61 | Answer: \(f(x) = \) \{ans_rule(10)\} \( + \) \{ans_rule(10)\} \( + \) \{ans_rule(10)\} \( + \) \{ans_rule(10)\} \( + \) \{ans_rule(10)\} \(+ \cdots\) |
62 | Answer: \(f(x) = \) \{ans_rule(8)\} \( + \) \{ans_rule(12)\} \( + \) \{ans_rule(12)\} \( + \) \{ans_rule(12)\} \( + \) \{ans_rule(14)\} \(+ \cdots\) |
| 62 | $HR |
63 | $HR |
| 63 | What is the radius of convergence? $BR |
64 | What is the radius of convergence? $BR |
| 64 | Answer: \(R = \) \{ans_rule(20)\} |
65 | Answer: \(R = \) \{ans_rule(10)\} |
| 65 | $HR |
|
|
| 66 | END_TEXT |
66 | END_TEXT |
| 67 | Context()->normalStrings; |
67 | Context()->normalStrings; |
| 68 | |
68 | |
| 69 | ##################################################################### |
69 | ##################################################################### |
| 70 | |
70 | |
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