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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x^2}{1+x^2}), which codomain element is missed?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\frac{x^2}{1+x^2}), तो कौन सा सहप्रांत अवयव छूटता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1)(1)
Step 1: At (x=0), (0) is obtained, and at (x=1), (\frac{1}{2}) is obtained. Step 2: (\frac{x^2}{1+x^2}<1) for every real (x), so (1) is never obtained. Step 3: When the denominator is larger than the numerator, check endpoint limit values carefully.चरण 1: (x=0) पर (0) मिलता है और (x=1) पर (\frac{1}{2}) मिलता है। चरण 2: (\frac{x^2}{1+x^2}<1) हर वास्तविक (x) के लिए है, इसलिए (1) कभी नहीं मिलता। चरण 3: जहाँ हर अंश से बड़ा हो, वहाँ अंतिम सीमा मान को सावधानी से देखें।
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