limit as x approaches-4 of (x)^2

{ "query": { "display": "$$\\lim_{x\\to\\:-4}\\left(\\left(x\\right)^{2}\\right)$$", "symbolab_question": "BIG_OPERATOR#\\lim _{x\\to -4}((x)^{2})" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Limits", "subTopic": "SingleVar", "default": "16", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\lim_{x\\to\\:-4}\\left(x^{2}\\right)=16$$", "input": "\\lim_{x\\to\\:-4}\\left(x^{2}\\right)", "steps": [ { "type": "step", "primary": "Plug in the value $$x=-4$$", "result": "=\\left(-4\\right)^{2}", "meta": { "title": { "extension": "Limit properties - if the limit of f(x), and g(x) exists, then:<br/>$$\\bullet\\quad\\lim_{x\\to\\:a}\\left(x\\right)=a$$<br/>$$\\bullet\\quad\\lim_{x\\to{a}}[c\\cdot{f\\left(x\\right)}]=c\\cdot\\lim_{x\\to{a}}{f\\left(x\\right)}$$<br/>$$\\bullet\\quad\\lim_{x\\to{a}}[\\left(f\\left(x\\right)\\right)^c]=\\left(\\lim_{x\\to{a}}{f\\left(x\\right)}\\right)^c$$<br/>$$\\bullet\\quad\\lim_{x\\to{a}}[f\\left(x\\right)\\pm{g\\left(x\\right)}]=\\lim_{x\\to{a}}{f\\left(x\\right)}\\pm\\lim_{x\\to{a}}{g\\left(x\\right)}$$<br/>$$\\bullet\\quad\\lim_{x\\to{a}}[f\\left(x\\right)\\cdot{g\\left(x\\right)}]=\\lim_{x\\to{a}}{f\\left(x\\right)}\\cdot\\lim_{x\\to{a}}{g\\left(x\\right)}$$<br/>$$\\bullet\\quad\\lim_{x\\to{a}}\\left(\\frac{f\\left(x\\right)}{g\\left(x\\right)}\\right)=\\frac{\\lim_{x\\to{a}}{f\\left(x\\right)}}{\\lim_{x\\to{a}}{g\\left(x\\right)}},\\:$$where $$\\lim_{x\\to{a}}g\\left(x\\right)\\neq0$$" } } }, { "type": "interim", "title": "Simplify $$\\left(-4\\right)^{2}:{\\quad}16$$", "input": "\\left(-4\\right)^{2}", "result": "=16", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(-a\\right)^{n}=a^{n},\\:$$if $$n$$ is even", "secondary": [ "$$\\left(-4\\right)^{2}=4^{2}$$" ], "result": "=4^{2}" }, { "type": "step", "primary": "$$4^{2}=16$$", "result": "=16" } ], "meta": { "solvingClass": "Solver", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s74VAHsj1tUmX5qQh5thgQZM0ag8T1MwTer44+aCS/ZFArolMr5JLBSbBMnU/0nIUZ1sD7NfhsPe7eDHrmjY0mE5dZzn4AQe6NSqf9BMtMRo7F3DenEWojLSGXYMDcAl7b" } } ], "meta": { "solvingClass": "Limits", "practiceLink": "/practice/limits-practice", "practiceTopic": "Limits" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "yes" }, "showViewLarger": true } }, "meta": { "showVerify": true } }