Given the function f defined by f(x) = { ((((2e^x )/(e^x −1)),x≠ 0)),((0, x = 0)) :} (i) study the differentiability of f at x = 0. (ii) Show that the point (0,1) is the centre of symetry to the curve of f.


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Question Number 141340 by physicstutes last updated on 17/May/21
$Given the function f defined by f(x) = { ((((2e^x )/(e^x −1)),x≠ 0)),((0, x = 0)) :} (i) study the differentiability of f at x = 0. (ii) Show that the point (0,1) is the centre of symetry to the curve of f.$
$Given the function f defined by$ $f (x) = {\begin{cases} \frac{2 e^{x}}{e^{x} - 1}, x \neq 0 \\ 0, x = 0 \end{cases}$ $(i) study the differentiability of f at x = 0 .$ $(ii) Show that the point (0, 1) is the centre of symetry to the$ $curve of f .$
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