Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacI % cacaWG4bGaaiykaiabg2da9maaceaaeaqabeaadaWcaaqaaiaaioda % cqGHsisldaGcaaqaaiaaisdacqGHsislcaWG4baaleqaaaGcbaGaaG % inaaaacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa % ae4AaiaabIgacaqGPbGaaeiiaiaabccacaqGGaGaamiEaiabgcMi5k % aaicdaaeaadaWcaaqaaiaaigdaaeaacaaI0aaaaiaabccacaqGGaGa % aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca % qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa % bccacaqGGaGaaeiiaiaabUgacaqGObGaaeyAaiaabccacaqGGaGaae % iiaiaabccacaWG4bGaeyypa0JaaGimaaaacaGL7baaaaa!6437! f(x) = \left\{ \begin{array}{l} \frac{{3 - \sqrt {4 - x} }}{4}{\rm{ khi }}x \ne 0\\ \frac{1}{4}{\rm{ khi }}x = 0 \end{array} \right.\). Khi đó f’(0)là kết quả nào sau đây?
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaCbeaeaaci % GGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaaabeaakmaa % laaabaGaamOzamaabmaabaGaamiEaaGaayjkaiaawMcaaiabgkHiTi % aadAgadaqadaqaaiaaicdaaiaawIcacaGLPaaaaeaacaWG4bGaeyOe % I0IaaGimaaaacqGH9aqpdaWfqaqaaiGacYgacaGGPbGaaiyBaaWcba % GaamiEaiabgkziUkaaicdaaeqaaOWaaSaaaeaadaWcaaqaaiaaioda % cqGHsisldaGcaaqaaiaaisdacqGHsislcaWG4baaleqaaaGcbaGaaG % inaaaacqGHsisldaWcaaqaaiaaigdaaeaacaaI0aaaaaqaaiaadIha % aaGaeyypa0ZaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacq % GHsgIRcaaIWaaabeaakmaalaaabaGaaGOmaiabgkHiTmaakaaabaGa % aGinaiabgkHiTiaadIhaaSqabaaakeaacaaI0aGaamiEaaaaaaa!656D \mathop {\lim }\limits_{x \to 0} \frac{{f\left( x \right) - f\left( 0 \right)}}{{x - 0}} = \mathop {\lim }\limits_{x \to 0} \frac{{\frac{{3 - \sqrt {4 - x} }}{4} - \frac{1}{4}}}{x} = \mathop {\lim }\limits_{x \to 0} \frac{{2 - \sqrt {4 - x} }}{{4x}}\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaC % beaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaaa % beaakmaalaaabaWaaeWaaeaacaaIYaGaeyOeI0YaaOaaaeaacaaI0a % GaeyOeI0IaamiEaaWcbeaaaOGaayjkaiaawMcaamaabmaabaGaaGOm % aiabgUcaRmaakaaabaGaaGinaiabgkHiTiaadIhaaSqabaaakiaawI % cacaGLPaaaaeaacaaI0aGaamiEamaabmaabaGaaGOmaiabgUcaRmaa % kaaabaGaaGinaiabgkHiTiaadIhaaSqabaaakiaawIcacaGLPaaaaa % Gaeyypa0ZaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGH % sgIRcaaIWaaabeaakmaalaaabaGaamiEaaqaaiaaisdacaWG4bWaae % WaaeaacaaIYaGaey4kaSYaaOaaaeaacaaI0aGaeyOeI0IaamiEaaWc % beaaaOGaayjkaiaawMcaaaaacqGH9aqpdaWfqaqaaiGacYgacaGGPb % GaaiyBaaWcbaGaamiEaiabgkziUkaaicdaaeqaaOWaaSaaaeaacaaI % XaaabaGaaGinamaabmaabaGaaGOmaiabgUcaRmaakaaabaGaaGinai % abgkHiTiaadIhaaSqabaaakiaawIcacaGLPaaaaaGaeyypa0ZaaSaa % aeaacaaIXaaabaGaaGymaiaaiAdaaaGaaiOlaaaa!7513! = \mathop {\lim }\limits_{x \to 0} \frac{{\left( {2 - \sqrt {4 - x} } \right)\left( {2 + \sqrt {4 - x} } \right)}}{{4x\left( {2 + \sqrt {4 - x} } \right)}} = \mathop {\lim }\limits_{x \to 0} \frac{x}{{4x\left( {2 + \sqrt {4 - x} } \right)}} = \mathop {\lim }\limits_{x \to 0} \frac{1}{{4\left( {2 + \sqrt {4 - x} } \right)}} = \frac{1}{{16}}.\)