Problem 50a

% MathType@MTEF@2@1@+=

% feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn

% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr

% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9

% vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x

% fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe

% qaamaaxababaGaciiBaiaacMgacaGGTbaaleaacaWG4bGaeyOKH4Qa

% aGimamaaCaaameqabaGaey4kaScaaaWcbeaakmaalaaabaGaaGymaa

% qaamaakaaabaGaaGOmaaWcbeaakmaalaaabaWaaqWaaeaaciGGZbGa

% aiyAaiaac6gacaWG4baacaGLhWUaayjcSdaabaGaamiEaaaaaaGaey

% ypa0Jaey4kaSYaaSaaaeaacaaIXaaabaWaaOaaaeaacaaIYaaaleqa

% aaaakiabg2da9iaaicdacaGGUaGaaG4naiaaicdacaaI3aaabaWaaC

% beaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGHsgIRcaaIWaWa

% aWbaaWqabeaacqGHsislaaaaleqaaOWaaSaaaeaacaaIXaaabaWaaO

% aaaeaacaaIYaaaleqaaOWaaSaaaeaadaabdaqaaiGacohacaGGPbGa

% aiOBaiaadIhaaiaawEa7caGLiWoaaeaacaWG4baaaaaacqGH9aqpcq

% GHsisldaWcaaqaaiaaigdaaeaadaGcaaqaaiaaikdaaSqabaaaaOGa

% eyypa0JaeyOeI0IaaGimaiaac6cacaaI3aGaaGimaiaaiEdaaaGaay

% 5Eaaaaaa@6B9F@

\[\left\{ \begin{align}

  & \underset{x\to {{0}^{+}}}{\mathop{\lim }}\,\frac{1}{\sqrt{2}\frac{\left| \sin x \right|}{x}}=+\frac{1}{\sqrt{2}}=0.707 \\ 

 & \underset{x\to {{0}^{-}}}{\mathop{\lim }}\,\frac{1}{\sqrt{2}\frac{\left| \sin x \right|}{x}}=-\frac{1}{\sqrt{2}}=-0.707 \\ 

\end{align} \right.\]