What is the limit as x approaches 0 of ((e^{2x}*e^{3x}-1-5x))/(x^2) ?

The limit as x approaches 0 of ((e^{2x}*e^{3x}-1-5x))/(x^2) is 25/2

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limit as x approaches 0 of ((e^{2x}*e^{3x}-1-5x))/(x^2)

x \to 0 lim (\frac{( e ^{2 x} \cdot e ^{3 x} - 1 - 5 x )}{x ^{2}})

\frac{25}{2}

Decimal

12.5

Solution steps

x \to 0 lim (\frac{e ^{2 x} e ^{3 x} - 1 - 5 x}{x ^{2}})

e^{2 x} e^{3 x} = e^{5 x}

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

Apply L'Hopital's Rule

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

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{25 e ^{5 x}}{2})

= x \to 0 lim (\frac{25 e ^{5 x}}{2})

Plug in the value

x = 0

= \frac{25 e ^{5 \cdot 0}}{2}

Simplify

= \frac{25}{2}

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What is the limit as x approaches 0 of ((e^{2x}*e^{3x}-1-5x))/(x^2) ?
The limit as x approaches 0 of ((e^{2x}*e^{3x}-1-5x))/(x^2) is 25/2