values of $\frac{1}{x}$ for a lot of different fractional values of $x$. (Don’t forget to include negative values). The answer should be roughly half way between the value for the smallest positive value of x and the smallest negative value. What is your result?\
(c) If you are in a study group, compare your result with others in your group. Can you all agree on the same value?\
(d) What would you say to someone who claims that division by zero is “undefined”? Explain your answer, referring to your results in part (b).\

$dx^{2}$ IS ZERO SIMPLIFIES\
THE BINOMIAL THEOREM
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[**EXERCISE**]{}

[**2.6**]{}

(a). Write down the derivative functions (the slope function, remember?) $\frac{dy}{dx}$ for $y(x) = x, x^{2}, x^{3}, x^{4}$. (You worked these out in Subsection 2.1).\
(b) Guess what the derivative function is for $y(x) = x^{n}$ where $n$ stands for any positive integer (do not use a specific numerical value for $n$), and write down your answer.

We now help you work out the answer to Exercise 2.5(b), using the definition of the derivative in Eq. \[eq:deriv\]. The first step is to expand the product $(x + dx)^{n}$, remembering that all powers of $dx$ higher than the 