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

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

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limit as u approaches 0 of (sin(u))/u

u \to 0 lim (\frac{sin ( u )}{u})

1

Solution steps

u \to 0 lim (\frac{sin ( u )}{u})

Apply L'Hopital's Rule

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

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

Plug in the value

u = 0

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

Simplify

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

= 1

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

x \to 1 + lim (3 - x)

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

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

x \to 5 lim (4 x - 2)

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