What is the limit as x approaches infinity of 3x^{2/3} ?

The limit as x approaches infinity of 3x^{2/3} is infinity

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limit as x approaches infinity of 3x^{2/3}

x \to \infty lim (3 x^{\frac{2}{3}})

\infty

Solution steps

x \to \infty lim (3 x^{\frac{2}{3}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 3 \cdot x \to \infty lim (x^{\frac{2}{3}})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

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

Apply the common limit:

x \to \infty lim (x) = \infty

= 3 \infty^{\frac{2}{3}}

Simplify

3 \infty^{\frac{2}{3}} : \infty

= \infty

x \to 2 - lim (2 x - 2)

x \to 0 lim ((1 + x)^{2})

x \to 3 + lim (\frac{2}{( x - 3 ) ^{2}})

x \to 0 - lim (- 3 x + 2)

p \to 0 lim (\frac{ln ( 0.7 x ^{p} + 0.3 y ^{p} )}{p})

What is the limit as x approaches infinity of 3x^{2/3} ?
The limit as x approaches infinity of 3x^{2/3} is infinity