What is the limit as x approaches 1 of (3^x-3)/(x-1) ?

The limit as x approaches 1 of (3^x-3)/(x-1) is 3ln(3)

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limit as x approaches 1 of (3^x-3)/(x-1)

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

3 ln (3)

Decimal

3.29583 \dots

Solution steps

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

Apply L'Hopital's Rule

: x \to 1 lim (\frac{ln ( 3 ) \cdot 3 ^{x}}{1})

= x \to 1 lim (\frac{ln ( 3 ) \cdot 3 ^{x}}{1})

Plug in the value

x = 1

= \frac{ln ( 3 ) \cdot 3 ^{1}}{1}

Simplify

= 3 ln (3)

x \to 0 lim (\frac{π}{4})

x \to 0 + lim (x^{3 x^{2}})

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

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

x \to 2 lim (\frac{3 x + 5}{x - 2})

What is the limit as x approaches 1 of (3^x-3)/(x-1) ?
The limit as x approaches 1 of (3^x-3)/(x-1) is 3ln(3)