which limit below is equal to the slope m of the curve at the given point?\na. lim h→0 √10(10+h) - √10(10) /…

Explanation:

Step1: Recall the formula for the slope of the tangent line

The slope (m) of the tangent line to the curve (y = f(x)) at the point ((a,f(a))) is given by (m=\lim_{h\rightarrow0}\frac{f(a + h)-f(a)}{h}).

Step2: Identify (f(x)) and (a)

Here, (f(x)=\sqrt{10x}) and (a = 10). Then (f(10)=\sqrt{10\times10}=\sqrt{100} = 10) and (f(10 + h)=\sqrt{10(10 + h)}).

Step3: Substitute into the slope formula

Substituting (f(10 + h)) and (f(10)) into the formula (m=\lim_{h\rightarrow0}\frac{f(a + h)-f(a)}{h}), we get (m=\lim_{h\rightarrow0}\frac{\sqrt{10(10 + h)}-\sqrt{10\times10}}{h}).

Answer:

A. (\lim_{h\rightarrow0}\frac{\sqrt{10(10 + h)}-\sqrt{10\times10}}{h})