Scary Limit

Calculus Level 4

limx0{sin2(π2ax)}sec2(π2bx)\large \lim_{x\rightarrow 0} \left\{\sin^{2}\left(\dfrac{\pi}{2-ax}\right)\right\}^{\sec^{2}\left(\frac{\pi}{2-bx}\right)}

If the value of the above limit is in the form ek(a2b2)e^{k\left(\frac{a^2}{b^2}\right)}, where kk is a integer, then find 2017k-2017k.

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