# What is the swap curve

## Finding the equation of tangent line to the curve at the given point

**EDIT:** Let's clarify a couple of things.

The *slope* of the *secant line* between $(a, f(a))$ and $(x,f(x)))$ is $$\frac

The *slope* of the *tangent line* at $(a, f(a))$ is $$\lim_

To find the *equation* of a tangent line, one needs to use the point-slope formula, which I've explained below.

Now, in your case, $f(x) = \sqrt

If we try to evaluate this limit by just plugging in $x = 1$, we get $0/0$, which is a problem (dividing by zero is bad), so we need a new strategy.

Idea: When evaluating the limits of fractions, a good trick is to multiply the top and bottom by the "radical conjugate." So:

$$\begin

\frac<\sqrt

Now we can evaluate $$\lim_*slope* of the tangent line. If you want the equation of the tangent line, you need the point-slope formula, explained below.

The point-slope formula says that a line with slope $m$ that passes through $(x_0, y_0)$ has an equation of the form $$y - y_0 = m(x-x_0).$$

In your case, the tangent line passes through $(1,1)$, so you can plug in $x_0 = 1$, $y_0 = 1$. We'll also have the slope, $m$, from the previous section once we evaluate that limit (which I leave to you to do).