Question

I am not sure I understand the following instructions on my book (Calculus: The Classic Edition, by Swokowski):

"[a] Use Definition (3.1) to find the slope of the tangent line to the graph of the equation at the point of x-coordinate a. [b] Find an equation of the tangent line at P. [c] Sketch the graph and the tangent line at P."

Then, I am given:
y = square root of x; P(4, 2)

The Definition (3.1) refers to the following:
limit when h approaches 0 of [ f(a + h) - f(a) ] / h

The answer book says that [a] is 1/(2*sqrt(a)) and [b] is y = (1/4)x + 1

Answer 1

\[\lim_{h\to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}\] is a start

Answer 2

I have figured out part [b] although I'm not understanding part [a].