What is the limit as x approaches 0+of (7x)^{2x} ?

The limit as x approaches 0+of (7x)^{2x} is 1

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limit as x approaches 0+of (7x)^{2x}

x \to 0 + lim ((7 x)^{2 x})

1

Solution steps

x \to 0 + lim ((7 x)^{2 x})

Simplify

(7 x)^{2 x} : 4 9^{x} x^{2 x}

= x \to 0 + lim (4 9^{x} x^{2 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 (4 9^{x}) \cdot x \to 0 + lim (x^{2 x})

x \to 0 + lim (4 9^{x}) = 1

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

= 1 \cdot 1

Simplify

= 1

x \to 0 lim (1 - 4 x)

x \to 0 lim (\frac{x + 2}{x + 5})

x \to \infty lim (x^{60})

x \to - 5 lim (23)

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

What is the limit as x approaches 0+of (7x)^{2x} ?
The limit as x approaches 0+of (7x)^{2x} is 1