November International SAT MATH Discussion.

Math112358
Sun, 04 Nov 2012 23:04:11 +0000

Keep in mind that when we find the area under a curve using calculus, we are using a limit to approximate the area. Limits allow us to find solutions which although technically not true, are infinitely close to being true. For example, the difference between x > 2 and x >= 2 can be taken as lim (x->0) 2 - (2 + x).

This is similar to statistics where, if we are looking at a normal distribution, the proportion P(z=x), where x is any number between -1 and 1 inclusive, is taken to be zero because it is so small. For similar reasoning P(z<=x) = P(z<x), because the difference, P(z=x), is zero. The same works for a curve; the boundary of a bounded curve has an infinitely small area and because of this, it doesn’t matter whether we include it or not.

jkjk0202, the point (-1,1) would lie ON the boundary, that is the curve y=x^2. The shaded region for x = -1 would contain the points 1 < y < 4. Therefore, y is greater than x^2