The value of lim_x 02 ( 1- cos ⁡x cos ⁡2x [3] cos ⁡3x … … [10] cos ⁡10xx^2 ) is

Question

Accepted Answer

Correct answer: 55. (55) limx 02 ( 1-(1- z^22 !)(1- 4x^22 !)(1- 9x^22 !) ⋯(1- 1002^22 !)x^2 ) By expansion ( limx 0 0.05em 2(1-(1- x^22))(1- 12 4x^22)(1- 13 9x^22) … …(1- 110 100x^22)x^2) limx 02 ( (1-(1- x^22)(1- 2x^22)(1- 3x^22) … …(1- 10x^22))x^2 ) limx 0 0.05em 2(1-1+x^2( 12+ 22+ 32+ …+ 102))x^22( 12+ 22+ 32+ …+ 102)1+2+ … …+10= 10 112=55

$The value of lim_{x \to 0} 2 (\frac{1 - cos x cos 2 x 3 cos 3 x \dots \dots \cdot 10 cos 10 x}{x ^{2}}) is$

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