Đồ thị hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9maalaaabaGaamiEaiabgUcaRmaakaaabaGaamiEamaaCaaaleqa % baGaaGOmaaaakiabgUcaRiaaigdaaSqabaaakeaacaWG4bGaeyOeI0 % IaaGymaaaaaaa!403E! y = \frac{{x + \sqrt {{x^2} + 1} }}{{x - 1}}\) có bao nhiêu đường tiệm cận?
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Lời giải:
Báo saiĐiều kiện: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiabgc % Mi5kaaigdaaaa!3973! x \ne 1\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % iEaiabg2da9iaaigdaaaa!3B0F! \Rightarrow x = 1\) là đường TCĐ của đồ thị hàm số.
Ta có: \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci % GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcqGHRaWkcqGHEisP % aeqaaOWaaSaaaeaacaWG4bGaey4kaSYaaOaaaeaacaWG4bWaaWbaaS % qabeaacaaIYaaaaOGaey4kaSIaaGymaaWcbeaaaOqaaiaadIhacqGH % sislcaaIXaaaaiabg2da9maaxababaGaciiBaiaacMgacaGGTbaale % aacaWG4bGaeyOKH4Qaey4kaSIaeyOhIukabeaakmaalaaabaGaaGym % aiabgUcaRmaakaaabaGaaGymaiabgUcaRmaalaaabaGaaGymaaqaai % aadIhadaahaaWcbeqaaiaaikdaaaaaaaqabaaakeaacaaIXaGaeyOe % I0YaaSaaaeaacaaIXaaabaGaamiEaaaaaaGaeyypa0JaaGOmaaaa!5B27! \mathop {\lim }\limits_{x \to + \infty } \frac{{x + \sqrt {{x^2} + 1} }}{{x - 1}} = \mathop {\lim }\limits_{x \to + \infty } \frac{{1 + \sqrt {1 + \frac{1}{{{x^2}}}} }}{{1 - \frac{1}{x}}} = 2\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % yEaiabg2da9iaaikdaaaa!3B11! \Rightarrow y = 2\) là 1 đường TCN của đồ thị hàm số.
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci % GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcqGHsislcqGHEisP % aeqaaOWaaSaaaeaacaWG4bGaey4kaSYaaOaaaeaacaWG4bWaaWbaaS % qabeaacaaIYaaaaOGaey4kaSIaaGymaaWcbeaaaOqaaiaadIhacqGH % sislcaaIXaaaaiabg2da9maaxababaGaciiBaiaacMgacaGGTbaale % aacaWG4bGaeyOKH4QaeyOeI0IaeyOhIukabeaakmaalaaabaGaaGym % aiabgkHiTmaakaaabaGaaGymaiabgUcaRmaalaaabaGaaGymaaqaai % aadIhadaahaaWcbeqaaiaaikdaaaaaaaqabaaakeaacaaIXaGaeyOe % I0YaaSaaaeaacaaIXaaabaGaamiEaaaaaaGaeyypa0JaaGimaaaa!5B46! \mathop {\lim }\limits_{x \to - \infty } \frac{{x + \sqrt {{x^2} + 1} }}{{x - 1}} = \mathop {\lim }\limits_{x \to - \infty } \frac{{1 - \sqrt {1 + \frac{1}{{{x^2}}}} }}{{1 - \frac{1}{x}}} = 0\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Taam % yEaiabg2da9iaaicdaaaa!3B0F! \Rightarrow y = 0\) là 1 đường TCN của đồ thị hàm số.
Vậy đồ thị hàm số đã cho có 2 TCN và 1 TCĐ
Đề thi thử tốt nghiệp THPT QG môn Toán năm 2020
Tuyển chọn số 4