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Take $\frac{\pi }{2}$ out of the fraction
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$\lim_{x\to1}\left(\left(1-x\right)^{\cos\left(\frac{\pi}{2}x\right)}\right)$
Learn how to solve problems step by step online. Find the limit of (1-x)^cos((pix)/2) as x approaches 1. Take \frac{\pi }{2} out of the fraction. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.