The value of limx→∞ n2+1+nn4+n4+n4, is - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
0
B
1
C
-1
D
none of these

Solution:

we have,

$\begin{array}{l} lim_{n \to \infty} \frac{\sqrt{n^{2} + 1} + \sqrt{n}}{\sqrt[4]{n^{3} + n - \sqrt[4]{n}}} \\ = lim_{n \to \infty} \frac{n \{\sqrt{1 + \frac{1}{n^{2}}} + \frac{1}{\sqrt{n}}\}}{n^{3 / 4} \{\sqrt[4]{1 + \frac{1}{n^{2}}} - \frac{1}{\sqrt{n}}\}} \\ = lim_{n \to \infty} n^{1 / 4} \frac{\{\sqrt{1 + \frac{1}{n^{2}}} + \frac{1}{\sqrt{n}}\}}{\{\sqrt[4]{1 + \frac{1}{n^{2}}} - \frac{1}{\sqrt{n}}\}} = \infty \times 2 = \infty \end{array}$

The value of $lim_{x \to \infty} \frac{\sqrt{n^{2} + 1} + \sqrt{n}}{\sqrt[4]{n^{4} + n} + \sqrt[4]{n}}$ , is

Solution:

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