*Note:* Melissa caught a typo in my original post and it has been fixed below.

The function for this problem is $f(x)=\frac{1}{x}$. For parts (a), (b), and (c), you are supposed to compute slopes of chords, where the left endpoint of the chord always has $x$-value 3. In each part, the right endpoint moves closer to $x=3$. For (a), $\Delta x=.1$ since $3.1-3=.1$. To answer part (a), you need to compute

(1)You will end up with a number. You need to do something similar for parts (b) and (c) except the value for $\Delta x$ is smaller.

Next, you are supposed to compute the difference quotient for an arbitrary $\Delta x$ and then determine what happens as $\Delta x$ approaches 0. I'll get you started.

(2)On the last step, I got common denominators on the fractions in the original numerator. Now, clean this up and see if you can whack a factor of $\Delta x$. If you can do this, you can plug in 0 for $\Delta x$ to obtain the slope of the tangent line at $x=3$ (which is the same as the derivative at $x=3$, but don't really worry about that).