What is the limit as x approaches 0 of (2^{ax}-2)/x ?

The limit as x approaches 0 of (2^{ax}-2)/x is diverges

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limit as x approaches 0 of (2^{ax}-2)/x

x \to 0 lim (\frac{2 ^{a x} - 2}{x})

diverges

Solution steps

x \to 0 lim (\frac{2 ^{a x} - 2}{x})

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (\frac{2 ^{a x} - 2}{x}) = - \infty

x \to 0 - lim (\frac{2 ^{a x} - 2}{x}) = \infty

= diverges

x \to 0 + lim (x ln (6 x))

x \to - 2 lim (3 x^{2})

x \to 0 + lim ((x)^{\frac{1}{x}})

x \to 3 lim (\frac{5 - x}{x - 2})

x \to 0 lim (x arctan (x))

What is the limit as x approaches 0 of (2^{ax}-2)/x ?
The limit as x approaches 0 of (2^{ax}-2)/x is diverges