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

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

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limit as x approaches 0 of sin(x) 1/x

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

1

Solution steps

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

Simplify

sin (x) \frac{1}{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

\int_{1}^{2} \frac{15}{x ^{3} + 2 x} d x

\frac{d}{d x} (2 x ln (x + 1))

\int \frac{( ln ( z ) ) ^{5}}{z} d z

\int e^{- 12 x} d x

x \to 5 lim (\frac{7 x}{x - 5})

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