Question
Download Solution PDFx के मानों का सेट ज्ञात कीजिए जिसके लिए f(x) = cos x - x _____ में घटता हुआ है।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
- यदि f′(x) > 0 तो कहा जाता है कि फलन बढ़ता हुआ है।
- यदि f′(x) < 0 तो कहा जाता है कि फलन घटता हुआ है।
गणना:
दिया हुआ:
f(x) = cos x – x
x के संबंध में अवकलन करके हमें मिलता है
⇒ f’(x) = -sin x – 1
जैसा कि हम जानते हैं कि,
-1 ≤ sin x ≤ 1, x ∈ R के लिए
⇒ -1 ≤ -sin x ≤ 1, x ∈ R के लिए
⇒ -1 - 1 ≤ -sin x - 1 ≤ 1 - 1, x ∈ R के लिए
⇒ -2 ≤ f’(x) ≤ 0, x ∈ R के लिए
∴ f’(x) ≤ 0, x ∈ R के लिए
इसलिए f(x), x ∈ R या x ∈ (-∞,∞) में घटता हुआ है
Last updated on Jul 8, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.