What is the limit as x approaches 2 of (sin(4x-8))/(3x-6) ?

The limit as x approaches 2 of (sin(4x-8))/(3x-6) is 4/3

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limit as x approaches 2 of (sin(4x-8))/(3x-6)

x \to 2 lim (\frac{sin ( 4 x - 8 )}{3 x - 6})

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

x \to 2 lim (\frac{sin ( 4 x - 8 )}{3 x - 6})

Apply L'Hopital's Rule

: x \to 2 lim (\frac{cos ( 4 x - 8 ) \cdot 4}{3})

= x \to 2 lim (\frac{cos ( 4 x - 8 ) \cdot 4}{3})

Plug in the value

x = 2

= \frac{cos ( 4 \cdot 2 - 8 ) \cdot 4}{3}

cos (4 \cdot 2 - 8) \cdot 4 = 4

= \frac{4}{3}

\frac{d}{d x} (\frac{( e ^{x} )}{x})

f (x) = e^{x 7 x + 6}

\frac{7}{2 s ^{2 + 8}}

\int cos^{2 - 2} (x) d x

\int \frac{x ^{2} + 12 x - 1}{x ^{3} - x} d x

What is the limit as x approaches 2 of (sin(4x-8))/(3x-6) ?
The limit as x approaches 2 of (sin(4x-8))/(3x-6) is 4/3