// Numbas version: exam_results_page_options {"name": "True/false statements about limits of sequences", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [{"variables": ["t_statements", "f_statements", "statements", "statement_marks", "choices"], "name": "Statements"}], "variables": {"t_statements": {"group": "Statements", "templateType": "list of strings", "definition": "[ \"There exists a sequence with all terms greater than zero and with limit 0.\", \"A divergent sequence can have a convergent subsequence.\", \"A convergent sequence is bounded.\", \"If a sequence is not bounded, then it does not converge.\", \"If {$\\{x_{n+i}\\}$} diverges for some natural number $i$, then {$\\{x_n\\}$} diverges.\", \"It is possible for a sequence to be both increasing and decreasing.\", \"In a convergent sequence, all subsequences converge to the same limit.\", \"A bounded increasing sequence converges.\", \"A bounded decreasing sequence converges.\", \"A sequence with only a finite number of non zero terms converges to 0.\", \"If a sequence has the subsequence given by the even terms converges to the same limit as the subsequence of odd terms, then the sequence also converges to that limit.\", \"A set with a maximum element is necessarily bounded above.\", \"A set with a minimum element is necessarily bounded below.\", \"A finite set is bounded.\", \"A set that is not bounded has an infinite number of elements.\", \"A bounded set has both a least upper bound and a greatest lower bound.\" ]", "description": "", "name": "t_statements"}, "f_statements": {"group": "Statements", "templateType": "list of strings", "definition": "[ \"A bounded sequence is convergent.\", \"Every divergent sequence is unbounded.\", \"A convergent sequence is either increasing or decreasing.\", \"If {$\\{x_n\\}$} converges, then {$\\{x_{n+i}\\}$} could diverge for some natural number $i$.\", \"There exists a convergent sequence {$\\{x_n\\}$} with $x_n >0$ for all $n \\\\in \\\\mathbb{N}$ and limit $\\\\ell <0$.\", \"There exists a bounded increasing sequences that does not converge.\", \"All convergent sequences of positive terms converge to a value $> 0$.\", \"If {$\\{x_n\\}$} diverges, then {$\\{x_{n+i}\\}$} could converge for some natural number $i$.\", \"There exists a sequence that is not bounded but which converges.\", \"It is not possible for a sequence to be both increasing and decreasing.\", \"A set with a maximum element is necessarily bounded.\", \"A set with a minimum element is necessarily bounded.\", \"A bounded set necessarily has a maximum element.\", \"A bounded set necessarily has a minimum element.\", \"A bounded set never has a maximum element.\", \"A bounded set never has a minimum element.\", \"A set with an infinite number of elements cannot be bounded.\" ]", "description": "", "name": "f_statements"}, "statement_marks": {"group": "Statements", "templateType": "anything", "definition": "map([1,-1],x,t_statements)+map([-1,1],x,f_statements)", "description": "", "name": "statement_marks"}, "statements": {"group": "Statements", "templateType": "anything", "definition": "t_statements+f_statements", "description": "", "name": "statements"}, "choices": {"group": "Statements", "templateType": "anything", "definition": "shuffle(0..len(statements)-1)[0..8]", "description": "", "name": "choices"}}, "ungrouped_variables": [], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "True/false statements about limits of sequences", "showQuestionGroupNames": false, "functions": {}, "parts": [{"prompt": "\n \n \n

[[0]]

\n \n \n \n", "scripts": {}, "gaps": [{"displayType": "radiogroup", "minMarks": 0, "layout": {"type": "all", "expression": ""}, "choices": ["{statements[choices[0]]}", "{statements[choices[1]]}", "{statements[choices[2]]}", "{statements[choices[3]]}", "{statements[choices[4]]}", "{statements[choices[5]]}", "{statements[choices[6]]}", "{statements[choices[7]]}"], "variableReplacementStrategy": "originalfirst", "matrix": "map(statement_marks[x],x,choices)", "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "warningType": "none", "scripts": {}, "marks": 0, "type": "m_n_x", "maxMarks": 0, "shuffleAnswers": false, "showCorrectAnswer": true, "variableReplacements": [], "answers": ["True", "False"]}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "

Answer the following question on sequences and sets. Note that a sequence is said to be unbounded if it is not bounded.

\n

Note that every correct answer is worth 1 mark, but every wrong answer loses a mark.

", "tags": ["bounded sequences", "bounded sets", "checked2015", "convergence", "convergent sequences", "decreasing sequence", "divergence", "divergent sequences", "increasing sequence", "limits", "MAS1601", "monotone sequence", "monotonic sequence", "sequence", "sequences", "subsequence", "unbounded sequences"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "

5/07/2012:

\n

Added tags.

\n

21/07/2012:

\n

Added description.

\n

27/7/2012:

\n

Added tags.

\n

 24/12/2012:

\n

Checked choices, OK. Added tested1 tag.

\n

Also included escaped slashes in string variables including tex.

\n

28/01/2015:

\n

(OK) Adjusted questions on sequences and added questions on boundedness of sets.

\n

17/04/2015:

\n

(OK) Recast the statements as long text.

", "licence": "Creative Commons Attribution 4.0 International", "description": "

Multiple response question (4 correct out of 8) covering properties of convergent and divergent sequences and boundedness of sets. Selection of questions from a pool.

"}, "advice": "

You should be able to work out the correct answers from your notes.

", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}