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

The limit as x approaches 3 of (3-x)/(2^x-8) is -1/(8ln(2))

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

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

- \frac{1}{8 ln ( 2 )}

Decimal Notation

- 0.18033 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 3

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

Simplify

= - \frac{1}{8 ln ( 2 )}

x \to 0 + lim (cos^{2} (x) + 1)

t \to \frac{π}{4} lim (\frac{sin ( t )}{t})

x \to 1 lim (\frac{x ^{2} + 1}{x + 6})

x \to 8 lim (\frac{x ^{2} - 8 x}{x ^{2} - 7 x - 8})

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

What is the limit as x approaches 3 of (3-x)/(2^x-8) ?
The limit as x approaches 3 of (3-x)/(2^x-8) is -1/(8ln(2))