What is the limit as x approaches 0+of |(sin(x))/x | ?

The limit as x approaches 0+of |(sin(x))/x | is 1

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limit as x approaches 0+of |(sin(x))/x |

x \to 0 + lim (\frac{sin ( x )}{x})

1

Solution steps

x \to 0 + lim (\frac{sin ( x )}{x})

\frac{sin ( x )}{x}

is positive when

x \to 0 +

. Therefore

\frac{sin ( x )}{x} = \frac{sin ( x )}{x}

= x \to 0 + lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

= \frac{cos ( 0 )}{1}

Simplify

\frac{cos ( 0 )}{1} : 1

= 1

x \to - 9 lim (x + 9)

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

x \to 3 lim (2 x + 7)

x \to 0 lim (\frac{3 tan ( 2 x )}{x})

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

What is the limit as x approaches 0+of |(sin(x))/x | ?
The limit as x approaches 0+of |(sin(x))/x | is 1