What is the limit as x approaches 2 of (2^x-4)/(x-2) ?

The limit as x approaches 2 of (2^x-4)/(x-2) is 4ln(2)

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limit as x approaches 2 of (2^x-4)/(x-2)

x \to 2 lim (\frac{2 ^{x} - 4}{x - 2})

4 ln (2)

Decimal

2.77258 \dots

Solution steps

x \to 2 lim (\frac{2 ^{x} - 4}{x - 2})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 2

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

Simplify

= 4 ln (2)

y = e^{x}, y = x, x = 0, x = 2

\int \frac{6 x ^{2} + 13 x + 6}{( x + 2 ) ( x + 1 ) ^{2}} d x

y = e^{x^{3}}, (- 1, \frac{1}{e})

\frac{( y - 2 ) ^{3}}{( y ^{2} + 4 y ) ^{7}}

x \to + 3 lim (f (x))

What is the limit as x approaches 2 of (2^x-4)/(x-2) ?
The limit as x approaches 2 of (2^x-4)/(x-2) is 4ln(2)