Limits Continuity And Differentiability

$f(x) = (1 + x)^{\frac{2}{x}},$ for $x \neq 0$
$= e^2,$ for $x = 0$

$f(x) = \sin x - \cos x,$ for $x \neq 0$
$= -1,$ for $x = 0$

$f(x) = \dfrac{e^{\frac{1}{x}} - 1}{e^{\frac{1}{x}} + 1},$ for $x \neq 0$
$= -1,$ for $x = 0$

$f(x) = \dfrac{e^{5x} - e^{2x}}{\sin 3x},$ for $x \neq 0$
$= 1,$ for $x = 0$