Be F the function of domain D(f) = R - (a). It's known that the limit f(x), when x approaches a, it's L.
It's written Lim f(x) = L , if for every b>0, there is a c>0, such as, if 0< |x - a|< c, therefore |f(x) - L) < b.
x-->a
Based on those conditions, evaluate the statements below.
I. If f(x) = (x² - 3x + 2)/x - 1, if x is different from 1.
3, if x is 1. Therefore lim f(x) = 0
x-->1
II. In the function f(x) = x² - 4, if x is smaller than 1.
-1, if x = 1
3 - x, if x is greater than 1. We have that lim f(x) = -3
x-->1
III. Be F and G random functions, we can state that lim (f . g) to the power of (n) times x = (LM) to the power of (n), n belonging to the set of natural numbers, if lim f(x) - L and lim g(x) = M x-->a x-->a
x-->a
Challenge for @Caesercel
It's written Lim f(x) = L , if for every b>0, there is a c>0, such as, if 0< |x - a|< c, therefore |f(x) - L) < b.
x-->a
Based on those conditions, evaluate the statements below.
I. If f(x) = (x² - 3x + 2)/x - 1, if x is different from 1.
3, if x is 1. Therefore lim f(x) = 0
x-->1
II. In the function f(x) = x² - 4, if x is smaller than 1.
-1, if x = 1
3 - x, if x is greater than 1. We have that lim f(x) = -3
x-->1
III. Be F and G random functions, we can state that lim (f . g) to the power of (n) times x = (LM) to the power of (n), n belonging to the set of natural numbers, if lim f(x) - L and lim g(x) = M x-->a x-->a
x-->a
Challenge for @Caesercel
this poor child
