- #1
songoku
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- 335
- 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