What is the limit as x approaches 0+of (5x)^{3x} ?

The limit as x approaches 0+of (5x)^{3x} is 1

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limit as x approaches 0+of (5x)^{3x}

x \to 0 + lim ((5 x)^{3 x})

1

Solution steps

x \to 0 + lim ((5 x)^{3 x})

Simplify

(5 x)^{3 x} : 12 5^{x} x^{3 x}

= x \to 0 + lim (12 5^{x} x^{3 x})

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

With the exception of indeterminate form

= x \to 0 + lim (12 5^{x}) \cdot x \to 0 + lim (x^{3 x})

x \to 0 + lim (12 5^{x}) = 1

x \to 0 + lim (x^{3 x}) = 1

= 1 \cdot 1

Simplify

= 1

x^{2} y^{^{'}} = 2 x y + y^{2}

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

n = 0 \sum \infty 9 (\frac{3}{4})^{n}

y = x, 0, 4

x \to \infty lim (4 x)

What is the limit as x approaches 0+of (5x)^{3x} ?
The limit as x approaches 0+of (5x)^{3x} is 1