What is the limit as x approaches 0+of sin((1/x)^x) ?

The limit as x approaches 0+of sin((1/x)^x) is sin(1)

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limit as x approaches 0+of sin((1/x)^x)

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

sin (1)

Decimal

0.84147 \dots

Solution steps

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

Apply the Limit Chain Rule:

sin (1)

= sin (1)

x \to 9 lim (x^{2} - 81)

x \to 9 - lim (ln (x^{2} (10 - x)))

x \to 3 lim ([x - 3])

x \to 2 lim (\frac{∣ x - 1 ∣}{x - 1})

x \to 0 lim (\frac{x}{( x + 3 ) ^{2} - 9})

What is the limit as x approaches 0+of sin((1/x)^x) ?
The limit as x approaches 0+of sin((1/x)^x) is sin(1)