limit as x approaches-infinity of 2/x+1

{ "query": { "display": "$$\\lim_{x\\to\\:-\\infty\\:}\\left(\\frac{2}{x}+1\\right)$$", "symbolab_question": "BIG_OPERATOR#\\lim _{x\\to -\\infty }(\\frac{2}{x}+1)" }, "solution": { "level": "PERFORMED", "subject": "Calculus", "topic": "Limits", "subTopic": "SingleVar", "default": "1", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\lim_{x\\to\\:-\\infty\\:}\\left(\\frac{2}{x}+1\\right)=1$$", "input": "\\lim_{x\\to\\:-\\infty\\:}\\left(\\frac{2}{x}+1\\right)", "steps": [ { "type": "step", "primary": "$$\\lim_{x\\to{a}}[f\\left(x\\right)\\pm{g\\left(x\\right)}]=\\lim_{x\\to{a}}{f\\left(x\\right)}\\pm\\lim_{x\\to{a}}{g\\left(x\\right)}$$<br/>With the exception of indeterminate form", "result": "=\\lim_{x\\to\\:-\\infty\\:}\\left(\\frac{2}{x}\\right)+\\lim_{x\\to\\:-\\infty\\:}\\left(1\\right)", "meta": { "title": { "extension": "Indeterminate Forms:<br/>$$\\frac{\\pm\\infty}{\\pm\\infty}$$<br/>$$\\frac{0}{0}$$<br/>$$\\pm\\infty\\cdot0$$<br/>$$0^0$$<br/>$$1^{\\pm\\infty}$$<br/>$$\\infty^{0}$$<br/>$$\\infty-\\infty$$" } } }, { "type": "interim", "title": "$$\\lim_{x\\to\\:-\\infty\\:}\\left(\\frac{2}{x}\\right)=0$$", "input": "\\lim_{x\\to\\:-\\infty\\:}\\left(\\frac{2}{x}\\right)", "steps": [ { "type": "step", "primary": "Apply Infinity Property: $$\\lim_{x\\to-\\infty}\\left(\\frac{c}{x^a}\\right)=0$$", "result": "=0" } ], "meta": { "solvingClass": "Limits", "interimType": "Limits", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7+jbUbsVfpMbXIJ0UHfO5sW8yQ0stCqMVssrXgR2l7RDcHDPUHkVpSWakcDpNB5xGHI5S0StY1FdtOqqOPr0Te4JMK9mJAiMjl/1mWqGgvKjyKNertMk7CgVOMvzgcgt5ZuJKdCFsPJy1+5gBMEc9djmqm40qzyGVY+WsRGEnpKJarGDlHNgwSdrYmV8S+RDA90R1gV6IcPy0uw6Lbw78GGezmh25OJYWjI6t5+TWV14=" } }, { "type": "interim", "title": "$$\\lim_{x\\to\\:-\\infty\\:}\\left(1\\right)=1$$", "input": "\\lim_{x\\to\\:-\\infty\\:}\\left(1\\right)", "steps": [ { "type": "step", "primary": "$$\\lim_{x\\to{a}}{c}=c$$", "result": "=1" } ], "meta": { "solvingClass": "Limits", "interimType": "Limits" } }, { "type": "step", "result": "=0+1" }, { "type": "step", "primary": "Simplify", "result": "=1", "meta": { "solvingClass": "Solver" } } ], "meta": { "solvingClass": "Limits", "practiceLink": "/practice/limits-practice", "practiceTopic": "Limits" } }, "plot_output": { "meta": { "plotInfo": { "variable": "x", "plotRequest": "yes" }, "showViewLarger": true } }, "meta": { "showVerify": true } }