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

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

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limit as x approaches pi-of sin(x)

x \to π - lim (sin (x))

0

Solution steps

x \to π - lim (sin (x))

Plug in the value

x = π

= 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

\frac{\partial}{\partial x} (9 - x^{2} - y^{2})

\int \frac{6 x + 2}{3 x ^{2} + 2 x} d x

\int_{0}^{1} \frac{1}{3 - x ^{2}} d x

\int \frac{x ^{6}}{( 4 - x ^{7} ) ^{2}} d x

\frac{d}{d x} (7 sec (x) tan (x))

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