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Evaluate the following limit : \(\lim\limits_{\text x \to1}\cfrac{1+cos\pi\text x}{(1-\text x)^2} \)

lim(x→1) (1 + cos πx)/(1 - x)2

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Given \(\lim\limits_{\text x \to1}\cfrac{1+cos\pi\text x}{(1-\text x)^2} \)

Now, x→1, then x - 1→0, let x - 1 = y

Hence, \(\lim\limits_{\text x \to1}\cfrac{1+cos\pi\text x}{(1-\text x)^2} \) = \(\cfrac{\pi^2}2\)

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