If L=limx→0 8x8(1−cosx22−cosx24+cosx22, cosx24) then 1L

Limx→0⁡8x81−cos⁡12x21−cos⁡14x2 =8⋅Limx→0⁡1−cos⁡12x2x22⋅Limx→01−cos⁡14x2x22=8⋅1222×1422=132

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If $L = \lim_{x \to 0} \frac{8}{x^{8}} (1 - \cos \frac{x^{2}}{2} - \cos \frac{x^{2}}{4} + \cos \frac{x^{2}}{2}, \cos \frac{x^{2}}{4})$ then $\frac{1}{L}$

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answer is 32.

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Detailed Solution

$\underset{x \to 0}{Lim} \frac{8}{x^{8}} [1 - \cos \frac{1}{2} x^{2}] [1 - \cos \frac{1}{4} x^{2}] = 8 \cdot \underset{x \to 0}{Lim} \frac{1 - \cos \frac{1}{2} x^{2}}{{(x^{2})}^{2}} \cdot \underset{x \to 0}{Lim} \frac{1 - \cos \frac{1}{4} x^{2}}{{(x^{2})}^{2}}$