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

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

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

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

8 ln (2)

Decimal

5.54517 \dots

Solution steps

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

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)

\int \frac{8}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

f (x) = \frac{5}{x}

\frac{d ^{2} x}{d t ^{2}} + 2 \frac{d x}{d t} + x = 6 e^{- t}

(\frac{x + 12}{x - 12})^{5}

\frac{d}{d x} (9 x (- 2)^{2} - 3 x (- 2) 1)

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