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

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

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limit as x approaches 0 of ((ee^{-ax}-e^{-bx}))/x

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

diverges

Solution steps

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

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

= diverges

f (x) = x^{3} - 3 x + 1

x = 36 - y^{2}, x = y^{2} - 36

\int t - cos (t) d t

\frac{d}{d x} (\frac{3 x ^{2} - 18 x + 25}{x ^{2} - 6 x + 8})

\int \frac{4 x - 2}{( 4 x ^{2} - 4 x + 2 ) ^{4}} d x

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