4. Use the inequality | sin x|


Basic Real Analysis 1


4. Use the inequality | sin x|< |x| for x ER to show that the sine function is continuous<br>at x = 0. Use this fact and the identity<br>sin x - sin u =<br>2 sin<br>CoS<br>|<br>to prove that the sine function is continuous at any point of u E R.<br>

Extracted text: 4. Use the inequality | sin x|< |x|="" for="" x="" er="" to="" show="" that="" the="" sine="" function="" is="" continuous="" at="" x="0." use="" this="" fact="" and="" the="" identity="" sin="" x="" -="" sin="" u="2" sin="" cos="" |="" to="" prove="" that="" the="" sine="" function="" is="" continuous="" at="" any="" point="" of="" u="" e="">

Jun 04, 2022
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