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

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

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

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

diverges

Solution steps

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

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

= diverges

3 (5^{x})

\int_{0}^{2} (2 x - 5)^{2} d x

\frac{d}{d x} ((\frac{3 x + 2}{x - 1})^{7})

y^{^{'}} = \frac{3 x ^{4} + y ^{4}}{x y ^{3}}

f (x) = \frac{1}{5 + 3 x}, (- 1, \frac{1}{2})

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