What is the limit as x approaches 0 of (ln(10x+1))/x ?

The limit as x approaches 0 of (ln(10x+1))/x is 10

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limit as x approaches 0 of (ln(10x+1))/x

x \to 0 lim (\frac{ln ( 10 x + 1 )}{x})

10

Solution steps

x \to 0 lim (\frac{ln ( 10 x + 1 )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{\frac{10}{10 x + 1}}{1})

= x \to 0 lim (\frac{\frac{10}{10 x + 1}}{1})

Plug in the value

x = 0

= \frac{\frac{10}{10 \cdot 0 + 1}}{1}

Simplify

= 10

x \to 0 lim (1 - \frac{tan ( 3 x )}{x})

x \to 4 + lim (10 - 2 x)

x \to - 2 lim (\frac{3}{( x + 2 ) ^{2}})

x \to - 6 lim (x + 4)

x \to 0 + lim (x^{2} (ln (x))^{2})

What is the limit as x approaches 0 of (ln(10x+1))/x ?
The limit as x approaches 0 of (ln(10x+1))/x is 10