What is the limit as x approaches 5 of (2^x-32)/(x-5) ?

The limit as x approaches 5 of (2^x-32)/(x-5) is 32ln(2)

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limit as x approaches 5 of (2^x-32)/(x-5)

x \to 5 lim (\frac{2 ^{x} - 32}{x - 5})

32 ln (2)

Decimal

22.18070 \dots

Solution steps

x \to 5 lim (\frac{2 ^{x} - 32}{x - 5})

Apply L'Hopital's Rule

= x \to 5 lim (\frac{ln ( 2 ) \cdot 2 ^{x}}{1})

Plug in the value

x = 5

= \frac{ln ( 2 ) \cdot 2 ^{5}}{1}

Simplify

= 32 ln (2)

What is the limit as x approaches 5 of (2^x-32)/(x-5) ?
The limit as x approaches 5 of (2^x-32)/(x-5) is 32ln(2)