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.