What is the limit as x approaches 0 of x(5^{1/x}-1) ?

The limit as x approaches 0 of x(5^{1/x}-1) is diverges

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limit as x approaches 0 of x(5^{1/x}-1)

x \to 0 lim (x (5^{\frac{1}{x}} - 1))

diverges

Solution steps

x \to 0 lim (x (5^{\frac{1}{x}} - 1))

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

then the limit does not exist

x \to 0 + lim (x (5^{\frac{1}{x}} - 1)) = \infty

x \to 0 - lim (x (5^{\frac{1}{x}} - 1)) = 0

= diverges

x \to - 6 lim (\frac{x ^{2} + 15 x + 54}{- 54 - 3 x + x ^{2}})

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

x \to - d lim (2 x^{3} + 3 x - 1)

x \to 3 lim (\frac{2 x - 11}{x - 3})

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

What is the limit as x approaches 0 of x(5^{1/x}-1) ?
The limit as x approaches 0 of x(5^{1/x}-1) is diverges