JEE PYQ: Limits Question 28
Question 28 - 2019 (09 Jan Shift 1)
$\lim_{y \to 0} \frac{\sqrt{1 + \sqrt{1 + y^4}} - \sqrt{2}}{y^4}$
(1) exists and equals $\frac{1}{4\sqrt{2}}$
(2) exists and equals $\frac{1}{2\sqrt{2}(\sqrt{2}+1)}$
(3) exists and equals $\frac{1}{2\sqrt{2}}$
(4) does not exist
Show Answer
Answer: (1)
Solution
Rationalising twice: $= \lim_{y\to 0}\frac{1+y^4 - 1}{y^4\left(\sqrt{1+\sqrt{1+y^4}}+\sqrt{2}\right)\left(\sqrt{1+y^4}+1\right)} = \frac{1}{2\sqrt{2} \times 2} = \frac{1}{4\sqrt{2}}$.
BETA
