Question
Download Solution PDF\(\rm \lim_{x\rightarrow \infty}{x^4 + 3x^2 + 5\over x^4 +x^2 -6}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
L - हॉस्पिटल का नियम:
यदि सीमा \({0\over 0}\) या \({\pm\infty\over \pm\infty}\) हो जाती है, तो इसे अंश और हर का अवकलन करके हल किया जाता है।
गणना:
सीमाओं को रखने पर हमें निम्न प्राप्त होता है
\(\rm \lim_{x\rightarrow \infty}{x^4 + 3x^2 + 5\over x^4 +x^2 -6}\) = \(\infty\over\infty\)
L हॉस्पिटल नियम को लागू करने पर
L(अर्थात्) = \(\rm \lim_{x\rightarrow \infty}{4x^3 + 6x\over 4x^3 +2x}\) = \(\rm \lim_{x\rightarrow \infty}{4x^2+ 6\over 4x^2 +2}\) = \(\infty\over \infty\)
फिर से L हॉस्पिटल नियम को लागू करने पर
⇒ L = \(\rm \lim_{x\rightarrow \infty}{8x\over 8x}\)
⇒ \(\rm \lim_{x\rightarrow \infty}1\)
∴ L = 1
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