What is the limit as x approaches 0 of (2x)/(3x) ?

The limit as x approaches 0 of (2x)/(3x) is 2/3

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limit as x approaches 0 of (2x)/(3x)

x \to 0 lim (\frac{2 x}{3 x})

\frac{2}{3}

Decimal Notation

0.66666 \dots

Solution steps

x \to 0 lim (\frac{2 x}{3 x})

Cancel the common factor:

x

= x \to 0 lim (\frac{2}{3})

x \to a lim c = c

= \frac{2}{3}

\int_{0}^{1} 5^{x} d x

sin (6 x)

y = \frac{1}{( t ^{4} + 1 ) ^{3}}

\frac{\partial}{\partial y} (\frac{2 x ^{2} y}{2 + x ^{2} y ^{2}})

n = 0 \sum \infty \frac{1}{ln ( n + 2 )}

What is the limit as x approaches 0 of (2x)/(3x) ?
The limit as x approaches 0 of (2x)/(3x) is 2/3