What is the limit as x approaches 2 of (3^x-9)/(x-2) ?

The limit as x approaches 2 of (3^x-9)/(x-2) is 9ln(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 2 of (3^x-9)/(x-2)

x \to 2 lim (\frac{3 ^{x} - 9}{x - 2})

9 ln (3)

Decimal Notation

9.88751 \dots

Solution steps

x \to 2 lim (\frac{3 ^{x} - 9}{x - 2})

Apply L'Hopital's Rule

: x \to 2 lim (\frac{ln ( 3 ) \cdot 3 ^{x}}{1})

= x \to 2 lim (\frac{ln ( 3 ) \cdot 3 ^{x}}{1})

Plug in the value

x = 2

= \frac{ln ( 3 ) \cdot 3 ^{2}}{1}

Simplify

= 9 ln (3)

\frac{\partial}{\partial x} (9 x e^{x^{2} + y^{2}})

\frac{d}{d x} (\frac{1}{5} x^{5} - 2 x^{3} + 3 x)

x \to - 1 lim (6 x + 3)

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

What is the limit as x approaches 2 of (3^x-9)/(x-2) ?
The limit as x approaches 2 of (3^x-9)/(x-2) is 9ln(3)