limit as x approaches 9+of (|x-9|)/(x-9)

{ "query": { "display": "$$\\lim_{x\\to\\:9+}\\left(\\frac{\\left|x-9\\right|}{x-9}\\right)$$", "symbolab_question": "BIG_OPERATOR#\\lim _{x\\to 9+}(\\frac{\\left|x-9\\right|}{x-9})" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Limits", "subTopic": "SingleVar", "default": "1", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\lim_{x\\to\\:9+}\\left(\\frac{\\left|x-9\\right|}{x-9}\\right)=1$$", "input": "\\lim_{x\\to\\:9+}\\left(\\frac{\\left|x-9\\right|}{x-9}\\right)", "steps": [ { "type": "step", "primary": "$$x-9$$ is positive when $$x\\to\\:9+$$. Therefore $$\\left|x-9\\right|=x-9$$", "result": "=\\lim_{x\\to\\:9+}\\left(\\frac{x-9}{x-9}\\right)" }, { "type": "step", "primary": "Simplify", "result": "=\\lim_{x\\to\\:9+}\\left(1\\right)" }, { "type": "step", "primary": "$$\\lim_{x\\to{a}}{c}=c$$", "result": "=1" } ], "meta": { "solvingClass": "Limits", "practiceLink": "/practice/limits-practice", "practiceTopic": "Limits" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "yes" }, "showViewLarger": true } }, "meta": { "showVerify": true } }