1)Suppose you use Newton’s method to solve an equation, and get an absurd
result. What can you do to get a solution to the equation?

2) Assume we are using the real number representation we discussed in class: a
sign and three decimal digits for a fraction, and a sign and two decimal digits
for an exponent. E.g. +123-45 means .123 x 10-45 .

Suppose we changed the representation by making the fraction 6 digits
long instead of three, but keeping the exponent at 2 digits. In this new
representation what is the closest number to zero that we can represent
exactly?

3)
Suppose you want to solve f(x, y) = x
2 + y3-10 using gradient descent.
Suppose your initial guess, (x0, y0), is (4, 1). If your next guess is (-4, y1),what is y1?



If you could help me with any or all, that would be great.

My try:

1) Change your initial guess?
2) .000001e(-99)
3) Well the gradient is (2x, 3y^2) and plugging that in gives with the initial (8,3), but I don't know what to do with this.