How to apply L.H. Rule?

Calculus Level 4

If A 2 = lim ⁡ x → 0 1 − ∏ i = 1 10 cos ⁡ ( i x ) x 2 \displaystyle \dfrac A2 = \lim_{x\to0} \dfrac{\displaystyle 1- \prod_{i=1}^{10} \cos(i x)}{x^2} , find A A .


The answer is 385.

Rishabh Deep Singh by Rishabh Deep Singh , 23, India

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1 solution

Pulkit Gupta
Feb 10, 2016

I did it by applying the series expansion for cos.

You may observe that the 1 cancels out and terms with x 2 \large x^{2} add up. We ignore higher order terms because they cancel out to zero.

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