Let $k\in \mathrm{ℝ}$. If $\lim _{x \rightarrow 0+}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}=e^6$, then the value of $k$ is [JEE Advanced 2024]

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Let \(k\in \mathrm{ℝ}\). If \(\lim _{x \rightarrow 0+}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}=e^6\), then the value of …