Derivative of f(x)=1/x at x=2 using the Limit Definition

  • Thread starter Thread starter eddieberto
  • Start date Start date
  • Tags Tags
    Definition
eddieberto
Messages
8
Reaction score
0
it tells me to use the definition

f(a)=limit...f(a+h)-f(a)
...h->0...__________
......h


to find the derivative of the given function at the indicated poin.
f(x)=1/x, a=2



I don't kno what to do
 
Physics news on Phys.org


its hard to read, try teh tex belwo (click on it)
lim_{h \rightarrow 0}\frac{f(a+h) - f(a)}{h}

try subsituting into the limit for your function evaulated at x = a, and x = a+h
 


this is how far i got and then i got lost

<br /> lim_{h \rightarrow 0}\frac{a-(a+h)}{h(a+h)(a)}<br />
and the answer is supos to be -1/4

im lost
 


you're not that far off, simplify the top line, then see what you cancel
 


thanks i got it
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top