Limit definition of derivatives:(
- Thread starter Wyzman23
- Start date
- Joined
- Nov 24, 2012
- Messages
- 3,021
Hello, and welcome to FMH! 
For part 1, you are instructed to find:
[MATH]f'(2)=\lim_{h\to0}\left(\frac{f(2+h)-f(2)}{h}\right)[/MATH]
where:
[MATH]f(x)=\frac{8}{x}[/MATH]
And so, we should write:
[MATH]f'(2)=\lim_{h\to0}\left(\frac{\dfrac{8}{2+h}-\dfrac{8}{2}}{h}\right)=\lim_{h\to0}\left(\frac{\dfrac{8}{2+h}-4}{h}\right)=\lim_{h\to0}\left(\frac{8-4(2+h)}{h(2+h)}\right)[/MATH]
Can you continue to simplify?
For part 1, you are instructed to find:
[MATH]f'(2)=\lim_{h\to0}\left(\frac{f(2+h)-f(2)}{h}\right)[/MATH]
where:
[MATH]f(x)=\frac{8}{x}[/MATH]
And so, we should write:
[MATH]f'(2)=\lim_{h\to0}\left(\frac{\dfrac{8}{2+h}-\dfrac{8}{2}}{h}\right)=\lim_{h\to0}\left(\frac{\dfrac{8}{2+h}-4}{h}\right)=\lim_{h\to0}\left(\frac{8-4(2+h)}{h(2+h)}\right)[/MATH]
Can you continue to simplify?