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

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

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

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

1

Solution steps

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

Apply exponent rules

= x \to 0 + lim (e^{2 x l n (s i n (x))})

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (x + 2 - 1)

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

x \to - 2 lim (\frac{4 x ^{2}}{x + 2})

x \to 1 lim (\frac{g ( x )}{x - 1})

x \to 1 - lim (\frac{x ^{2}}{x - 1})

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