What is the limit as x approaches 0 of (e^{5x}-1)/(x^2) ?

The limit as x approaches 0 of (e^{5x}-1)/(x^2) is diverges

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limit as x approaches 0 of (e^{5x}-1)/(x^2)

x \to 0 lim (\frac{e ^{5 x} - 1}{x ^{2}})

diverges

Solution steps

x \to 0 lim (\frac{e ^{5 x} - 1}{x ^{2}})

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

then the limit does not exist

x \to 0 + lim (\frac{e ^{5 x} - 1}{x ^{2}}) = \infty

x \to 0 - lim (\frac{e ^{5 x} - 1}{x ^{2}}) = - \infty

= diverges

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What is the limit as x approaches 0 of (e^{5x}-1)/(x^2) ?
The limit as x approaches 0 of (e^{5x}-1)/(x^2) is diverges