Show that the sequence of functions [f_n], defined on R for each n in N as the top half of the hyperbolae
y^2 - x^2 = 1/(n^2)
converges uniformly on R to f(x) = abs(x). What do you note about the differentiability of the function at x=0?
Show that the sequence of functions [f_n], defined on R for each n in N as the top half of the hyperbolae
y^2 - x^2 = 1/(n^2)
converges uniformly on R to f(x) = abs(x). What do you note about the differentiability of the function at x=0?
See as far the convergence is concerned i havent worked out it yet. But as for the differentiablity of is concerned you should not that the function is not differentiable at the point for the left hand derivative at is -1 whereas the R.H.D at is 1.