What is the limit as x approaches 0+of 5x^x ?

The limit as x approaches 0+of 5x^x is 5

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limit as x approaches 0+of 5x^x

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

5

Solution steps

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

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

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

Apply exponent rules

= 5 \cdot x \to 0 + lim (e^{x l n (x)})

Apply the Limit Chain Rule:

1

= 5 \cdot 1

Simplify

= 5

x \to \infty lim (\frac{( a x + b ) ^{2}}{( a - x ) ( b - x )})

x \to 0 lim (3 tan (x) ln (x))

x \to 3 - lim (\frac{3 - x}{∣ x - 3 ∣})

x \to + 0 lim (\frac{tan ( 8 x )}{x})

x \to 8 lim (2 x - 8)

What is the limit as x approaches 0+of 5x^x ?
The limit as x approaches 0+of 5x^x is 5