What is the limit as x approaches 0 of (ln(1+5x))/x ?

The limit as x approaches 0 of (ln(1+5x))/x is 5

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limit as x approaches 0 of (ln(1+5x))/x

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

5

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{\frac{5}{1 + 5 \cdot 0}}{1}

Simplify

= 5

y^{^{'}} - \frac{y}{x} = 0

\int (4 x + 3) \cdot (2 x^{2} + 3 x)^{3} d x

\int \frac{( x ^{3} )}{x ^{2} + 64} d x

\frac{d}{d x} ((3 x + 2) (x - 1)^{3})

y = x^{3} - 2 x + 1, (3, 22)

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