Question
Download Solution PDFx के मानों का सेट ज्ञात कीजिए जिसके लिए f(x) = tan-1 x _____ में बढ़ता 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) = tan-1 x
x के संबंध में अवकलन करके हमें मिलता है
जैसा कि हम जानते हैं कि, x ∈ R के लिए x2 > 0
⇒ x ∈ R के लिए 1 + x2 > 0
इसलिए 1 + x2, x∈ R के लिए धनात्मक मान देता है
अतः x ∈ R के लिए f’(x) > 0
इसलिए f(x), x ∈ R या x ∈ (-∞,∞) में बढ़ता हुआ है
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