What is the limit as x approaches 0.1 of (e^{5x}-1)/x ?

The limit as x approaches 0.1 of (e^{5x}-1)/x is 6.48721…

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limit as x approaches 0.1 of (e^{5x}-1)/x

x \to 0.1 lim (\frac{e ^{5 x} - 1}{x})

6.48721 \dots

Solution steps

x \to 0.1 lim (\frac{e ^{5 x} - 1}{x})

Plug in the value

x = 0.1

= \frac{e ^{5 \cdot 0.1} - 1}{0.1}

Simplify

= 6.48721 \dots

4 y^{^{''}} + 36 y^{^{'}} + 81 y = 0

- 3 x^{2} + 6 x - 2

y = 7 x^{2} - x^{3}

f^{^{'}} (x) = sec (2 x) tan (2 x)

\frac{d y}{d x} = 2 y (3 - x)

What is the limit as x approaches 0.1 of (e^{5x}-1)/x ?
The limit as x approaches 0.1 of (e^{5x}-1)/x is 6.48721…