What is the limit as x approaches 3 of (2^x-8)/(3-x) ?

The limit as x approaches 3 of (2^x-8)/(3-x) is -8ln(2)

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limit as x approaches 3 of (2^x-8)/(3-x)

x \to 3 lim (\frac{2 ^{x} - 8}{3 - x})

- 8 ln (2)

Decimal Notation

- 5.54517 \dots

Solution steps

x \to 3 lim (\frac{2 ^{x} - 8}{3 - x})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 3

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

Simplify

= - 8 ln (2)

y = 4 x, y = 4, y = \frac{4}{9} x^{2} 4

\int_{6}^{8} \frac{62}{( x - 6 ) ^{3}} d x

\frac{\partial}{\partial u} (u^{2} v)

\int 12 x^{3} (ln (4 x))^{2} d x

\int (3 x^{2} + 8) d x

What is the limit as x approaches 3 of (2^x-8)/(3-x) ?
The limit as x approaches 3 of (2^x-8)/(3-x) is -8ln(2)