- #1

songoku

- 2,351

- 340

- Homework Statement
- Please see below

- Relevant Equations
- Limit

Sequence Theorem

Derivative from first principle

##f'(x_0)## is defined as:

$$f'(x_0)=\lim_{h \rightarrow 0} \frac{f(x_0+h)-f(x_0)}{h}$$

or

$$f'(x_0)=\lim_{x \rightarrow x_0} \frac{f(x)-f(x_0)}{x-x_0}$$

I can imagine that as ##n \rightarrow \infty## the value of ##f(b_n)## and ##f(a_n)## will approach ##f(x_0)## so the value of the limit will be like tangent to graph ##f(x)## at point ##x_0##

But I don't know how to do it mathematically. The definition I know for derivative is the limit approaches 0 while the question is n approaches infinity. How to relate the question to the definition?

Thanks