# ICE 1

- Start a script that assigns
the integer 123456789012345678901234567890
to a variable
`a`. How many digits is that? What is \(2^64\)? - Make a function called
`f`that maps`x`to`1+x-x`. What is`f(1)`? What is`f(1e10)`? What is`f(1e20)`? - Make a function called
`dq`that evaluates the difference quotient that estimates the derivative of \(g(x)=x^2\) at 1 for a given step \(h\) In other words, the function should be $$\text{dq}(h) = \frac{(1+h)^2-1^2}h.$$ Evaluate \(\text{dq}(0.1)\), \(\text{dq}(10^{-8})\), \(\text{dq}(10^{-12})\), and \(\text{dq}(10^{-16})\).

Welcome to Math 583, Hacking Mathematics.