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

The limit as x approaches 2 of (x^x-4)/(x-2) is 4(ln(2)+1)

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

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

4 (ln (2) + 1)

Decimal

6.77258 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 2

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

Simplify

= 4 (ln (2) + 1)

\int \frac{1}{x \cdot ( x - 1 )} d x

\frac{\partial}{\partial x} (\frac{12 x}{y + 6})

\frac{ln ( 8 x )}{8 x}

8 x \cdot \frac{d y}{d x} = 2 x e^{x} - 8 y + 6 x^{2}

\int \frac{3}{e ^{x}} d x

What is the limit as x approaches 2 of (x^x-4)/(x-2) ?
The limit as x approaches 2 of (x^x-4)/(x-2) is 4(ln(2)+1)