Let f(x)=sqrt (x)-5 Then lim _(harrow 0)(f(2+h)-f(2))/(h)=

To find the limit \(\lim_{h \to 0} \frac{f(2+h) - f(2)}{h}\), we first need to determine the function \(f(x)\) and then evaluate the difference quotient.Given \(f(x) = \sqrt{x} - 5\), we can find \(f(2)\) and \(f(2+h)\): Now, we can substitute these values into the difference quotient: Simplifying the numerator, we have: To evaluate this limit, we can use the conjugate method. Multiply the numerator and denominator by the conjugate of the numerator: This simplifies to: As approaches 0, approaches . Therefore, the limit is: So, the correct answer is .