Nice to meet you everyone.
I’m an engineer of Korea, working on image object recognition.
Any help (especially about my English translation) would be welcomed.
pilhoon-at-gmail-dot-com

## 2015년 11월 17일 화요일

### Taylor’s Formula

If $$f(x) = a_0 + a_1 x + a_2 x^2 + \cdots$$,
$$a_n = \frac{f^{(n)}(0)}{n!}$$
with another base point
$$f(x) = f(b) + f’(b)(x-b) + \frac{f’’(b)}{2} (x-b)^2 + \frac{ f^{(3)}(b)}{3!}(x-b)^3 + \cdots$$
For example, $$\sqrt{x}$$ is not appropriate to expand at $$0$$ because it’s not differentiable at $$0$$. so use $$b= 1$$,
$$x^{\frac{1}{2}} = 1 + \frac{1}{2}(x-1) + \frac{ \left( \frac{1}{2} \right) \left( \frac{1}{2} - 1 \right) }{2!} (x-1)^2 + \cdots$$

#### 댓글 1개:

1. 어려운내용이 가득하네요...