// Numbas version: exam_results_page_options {"name": "Evaluate a limit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b"], "name": "Evaluate a limit", "tags": [], "advice": "

\$$\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{x-\\var{a}}{x^2-\\simplify{{a}+{b}}x+\\simplify{{a}*{b}}}\$$

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We can factorise the denominator

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\$$\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{x-\\var{a}}{(x-\\var{a})(x-\\var{b})}\$$

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Cancel out the common factor

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\$$\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{1}{x-\\var{b}}\$$

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Insert the value \$$\\var{a}\$$ in for \$$x\$$ to evaluate the limit

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\$$-\\frac{1}{\\simplify{{b}-{a}}}\$$

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", "rulesets": {}, "parts": [{"prompt": "

\$$\\displaystyle{\\lim_{x \\to \\var{a}}}\\frac{x-\\var{a}}{x^2-\\simplify{{a}+{b}}x+\\simplify{{a}*{b}}}\$$