What is the limit as x approaches 3 of x-0(sin(x))^x ?

The limit as x approaches 3 of x-0(sin(x))^x is 3

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limit as x approaches 3 of x-0(sin(x))^x

x \to 3 lim (x - 0 (sin (x))^{x})

3

Solution steps

x \to 3 lim (x - 0 \cdot (sin (x))^{x})

Plug in the value

x = 3

= 3 - 0 \cdot (sin (3))^{3}

Simplify

3 - 0 \cdot sin^{3} (3) : 3

= 3

x \to 3 lim (3 x - 5)

x \to 3 lim (\frac{1}{x ^{2} e ^{2}})

x \to 3 lim (- 5 x^{2} - 2 x + 1)

x \to 3 lim ((\frac{1}{x})^{x})

x \to 3 lim (1^{x})

What is the limit as x approaches 3 of x-0(sin(x))^x ?
The limit as x approaches 3 of x-0(sin(x))^x is 3