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फलन f(x) = (x + 1)cotx x = 0 पर सतत रहेगा यदि f(0) का मान ________ है।

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  3. e
  4. 1

Answer (Detailed Solution Below)

Option 3 : e
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संकल्पना:

एक फलन को सतत कहा जाता है यदि

गणना:

दिया गया:

f(x) = (x + 1)cotx

दोनों तरफ से log लेना

log (f(x)) = cot x log (x + 1)

x = 0 पर निरंतरता की जाँच के लिए

= 0/0

L--हॉस्पिटल नियम का उपयोग करना

⇒ log (f(0)) = 1

⇒ f(0) = e1 = e

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