Question

       

  Dada a função f(x)=X2, calcule f'(1)  

          f’(x0)  = lim  f(x)-f (x0) /X- x0

                      quando x tende a x0      

  

  

Answer 1

$\boxed{f(x)= x^{2} } \\ \\ f'(x)= \lim_{\Delta x \to 0} \frac{f(x+ \Delta x)-f(x)}{\Delta x} \\ \\ f'(x)=\lim_{\Delta x \to 0} \frac{f(x+ \Delta x)^2-x^2}{\Delta x} \\ \\ f'(x)=\lim_{\Delta x \to 0} \frac{x^2+2x \Deltax+ (\Delta x)^2-x^2}{\Delta x} \\ \\ f'(x)=\lim_{\Delta x \to 0} \frac{2x \Deltax+ (\Delta x)^2}{\Delta x} \\ \\ f'(x)=\lim_{\Delta x \to 0} (2x \Deltax+ \Delta x) \\ \\ \boxed{f'(x)=2x } \\ \\ \boxed{f'(1)=2.1=2}$