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

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

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

x \to 0 + lim ((tan (x))^{s i n (x)})

1

Solution steps

x \to 0 + lim ((tan (x))^{s i n (x)})

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 6 lim (\frac{2 x}{x ^{2} - 36})

x \to 0 + lim ((1 - 3 x)^{\frac{2}{x}})

x \to e + lim (\frac{1}{x ln ( x - 1 )})

x \to 3 lim (\frac{x + 1}{x - 3})

x \to 1 - lim (ln (x) ln (1 - x))

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