Chapter 9.6, Problem 91E

a.

To determine

To rationalize: The numerator of the rational expression $\frac{\sqrt{x+h}-\sqrt{x}}{h}$ and simplify.

b.

To determine

To evaluate: The value of the expression $\frac{1}{\sqrt{x+h}+\sqrt{x}}$ at $h=0$.

c.

To determine

The slope of the line tangent to the graph of $f\left(x\right)=\sqrt{x}$ at $x=4$.

d.

To determine

The value of $f\left(4\right)$ where $f\left(x\right)=\sqrt{x}$ and obtain the points on the graph at $x=4$.

e.

To determine

The equation of the line tangent to $f\left(x\right)=\sqrt{x}$ at $x=4$.

f.

To determine

To sketch: The function $f\left(x\right)=\sqrt{x}$ and the tangent line in the same plane.