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

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

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

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

b

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{b e ^{b x}}{1})

= x \to 0 lim (\frac{b e ^{b x}}{1})

Plug in the value

x = 0

= \frac{b e ^{b \cdot 0}}{1}

Simplify

= b

x \to + 1 lim (\frac{x}{( x - 1 )})

x \to 0 lim (\frac{x - 6}{x - 2})

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

\frac{d y}{d x} = 12

\frac{d}{d x} (x + \frac{1}{x + 2})

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