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The limit represents a derivative

The Correct Answer and Explanation is: To solve the given limit: lim⁡h→0sin⁡(5π3+h)+32h\lim_{{h \to 0}} \frac{{\sin\left(\frac{5\pi}{3} + h\right) + \frac{\sqrt{3}}{2}}}{h} we begin by comparing it to the standard definition of the…