Se $x \\to\u00a0 + \\infty $, ent\u00e3o $\\frac{{20}}{{x – 3}} \\to {0^ + }$, $2x + 7 \\to\u00a0 + \\infty $ e, consequentemente, $h\\left( x \\right) = 2x + 7 + \\frac{{20}}{{x – 3}} \\to\u00a0 + \\infty $.
\nIsto \u00e9: \\[\\mathop {\\lim }\\limits_{x \\to\u00a0 + \\infty } h\\left( x \\right) =\u00a0 + \\infty \\]
\nLogo, o gr\u00e1fico de $h$ n\u00e3o possui ass\u00edntota horizontal quando $x \\to\u00a0 + \\infty $.
\nNo entanto, $y = 2x + 7$ \u00e9 a equa\u00e7\u00e3o reduzida de uma ass\u00edntota obl\u00edqua do gr\u00e1fico de $h$ quando $x \\to\u00a0 + \\infty $.<\/p>\nDe forma an\u00e1loga, conclui-se que \\[\\mathop {\\lim }\\limits_{x \\to\u00a0 – \\infty } h\\left( x \\right) =\u00a0 – \\infty \\]
\nLogo, o gr\u00e1fico de $h$ n\u00e3o possui ass\u00edntota horizontal quando $x \\to\u00a0 – \\infty $.
\nNo entanto, $y = 2x + 7$ \u00e9\u00a0a equa\u00e7\u00e3o reduzida de uma ass\u00edntota obl\u00edqua do gr\u00e1fico de $h$ quando $x \\to\u00a0 – \\infty $.<\/p>\n
Se $x \\to {3^ – }$, ent\u00e3o $\\frac{{20}}{{x – 3}} \\to\u00a0 – \\infty $ e, consequentemente, $h\\left( x \\right) = 2x + 7 + \\frac{{20}}{{x – 3}} \\to\u00a0 – \\infty $.
\nIsto \u00e9: \\[\\mathop {\\lim }\\limits_{x \\to {3^ – }} h\\left( x \\right) =\u00a0 – \\infty \\]
\nDe forma an\u00e1loga, conclui-se que \\[\\mathop {\\lim }\\limits_{x \\to {3^ + }} h\\left( x \\right) =\u00a0 + \\infty \\]
\nLogo, a reta de equa\u00e7\u00e3o $x = 3$ \u00e9 uma equa\u00e7\u00e3o da ass\u00edntota vertical (bilateral)\u00a0do gr\u00e1fico de $h$ quando $x \\to 3$.
\n\u00ad<\/p>\n<\/li>\n