Question
Download Solution PDFयदि f(x) = e|x| तो निम्नलिखित में से कौन सा सही है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
- फलन की अवकलनीयता: एक फलन f(x) इसके डोमेन में x = a पर अवकलनीय तब होता है यदि इसका अवकलज a पर निरंतर होता है।
इसका अर्थ है कि f'(a) को मौजूद होना चाहिए, या समकक्ष रूप से:
। - मापांक फलन '| |' को निम्न रूप में परिभाषित किया गया है:
गणना:
मापांक फलन की परिभाषा का उपयोग करते हुए, हमारे पास है:
f(x) = ex, x ≥ 0
और f(x) = e-x, x < 0
अवकलजों के पहले सिद्धांत का उपयोग करते हुए हम पाते हैं कि:
और,
चूंकि
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