What is the limit as x approaches 3 of (1-cos(x))/x ?

The limit as x approaches 3 of (1-cos(x))/x is (1-cos(3))/3

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limit as x approaches 3 of (1-cos(x))/x

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

\frac{1 - cos ( 3 )}{3}

Decimal

0.66333 \dots

Solution steps

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

Plug in the value

x = 3

= \frac{1 - cos ( 3 )}{3}

x \to 3 lim (3 x^{2} + 6 x + 5)

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

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

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

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

What is the limit as x approaches 3 of (1-cos(x))/x ?
The limit as x approaches 3 of (1-cos(x))/x is (1-cos(3))/3