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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

z = 0

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

Simplify

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

= 1

x \to - 2 lim ((3 x + 8)^{x + 1})

x \to 0 lim (\frac{x}{∣ x ∣})

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

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

x \to 0 lim (arctan (2 x))

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