- #1
Genericcoder
- 131
- 0
let E = episolon and D = delta;
the problem is as follows:
let f(x) = (2x^2 - 3x + 3). prove that lim as x approaches 3 f(x) = 21,
we write |f(x) - 21| = |x^2 + 2x - 15| = |x + 5||x - 3|
to make this small, we need a bound on the size of |x + 5| when x is close to 3. For example,
if we arbitarily require that |x - 3| < 1 then
|x + 5| = |x - 3 + 8| <= |x - 3| + |8| < 1 + 8 = 9
to make E f(x) within E of 21, we want to have |x + 5| < 9 and |x - 3| < E/9
I don't understand how did he get E/9 |x - 3| < E/9 ?
the problem is as follows:
let f(x) = (2x^2 - 3x + 3). prove that lim as x approaches 3 f(x) = 21,
we write |f(x) - 21| = |x^2 + 2x - 15| = |x + 5||x - 3|
to make this small, we need a bound on the size of |x + 5| when x is close to 3. For example,
if we arbitarily require that |x - 3| < 1 then
|x + 5| = |x - 3 + 8| <= |x - 3| + |8| < 1 + 8 = 9
to make E f(x) within E of 21, we want to have |x + 5| < 9 and |x - 3| < E/9
I don't understand how did he get E/9 |x - 3| < E/9 ?