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

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

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

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

5 ln (5)

Decimal Notation

8.04718 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{ln ( 5 ) \cdot 5 ^{x + 1}}{1})

= x \to 0 lim (\frac{ln ( 5 ) \cdot 5 ^{x + 1}}{1})

Plug in the value

x = 0

= \frac{ln ( 5 ) \cdot 5 ^{0 + 1}}{1}

Simplify

= 5 ln (5)

\int_{0}^{\infty} 8 sin^{2} (x) d x

\int arctan (d) x d x

\frac{d}{d θ} (\frac{2}{1 - sin ( θ )})

x \to 5 lim (x^{2} + 5 x + 8)

\frac{x}{1 + 4 x ^{2}}

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