Evaluate a limit by recognizing it as a slight variation of the limit definition of the derivative.

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Evaluating a Limit Using the Definition of the Derivative

Derivatives warmup

If \( f \) is differentiable and \( f(x_0) = 0 \), find \( \lim_{h\to 0} \frac{f(x_0 + h)}{7h} \).

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Tests the student's ability to recognize the difference quotient and apply the definition of the derivative algebraically.

This is a standard introductory calculus problem designed to test recognition of the formal definition of the derivative.