What is the limit as t approaches 0+of (sin(t))^t ?

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

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limit as t approaches 0+of (sin(t))^t

t \to 0 + lim ((sin (t))^{t})

1

Solution steps

t \to 0 + lim ((sin (t))^{t})

Apply exponent rules

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

Apply the Limit Chain Rule:

1

= 1

x \to 0 lim (+ (cos (2 x)) \frac{1}{x})

x \to 0 lim (\frac{1}{x} ln (x))

x \to 0 lim (\frac{( sin ( 5 x ) )}{sin ( 4 x )})

x \to 6 - lim (\frac{x - [ x ]}{x - 6})

x \to 0 lim (\frac{1}{e ^{- x} - 1})

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