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

The limit as x approaches 0 of sin(pi) is 0

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limit as x approaches 0 of sin(pi)

x \to 0 lim (sin (π))

0

Solution steps

x \to 0 lim (sin (π))

x \to a lim c = c

= sin (π)

Use the following trivial identity:

sin (π) = 0

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

t \to 0 lim (\frac{sin ( - 3 t )}{t})

x \to 0 - lim (x^{2} \cdot ln (- x))

x \to 0 lim ((\frac{1}{x}) (\frac{1}{3} - \frac{1}{x + 9}))

x \to 1 lim (\frac{x - 1}{2})

x \to - \frac{π}{2} - lim (sec (x))

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