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

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

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limit as x approaches 0 of sin(0)

x \to 0 lim (sin (0))

0

Solution steps

x \to 0 lim (sin (0))

x \to a lim c = c

= sin (0)

Use the following trivial identity:

sin (0) = 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} (200 (y - x^{2}))

x \to - 2 lim (\frac{x - 1}{x ^{2} - 4})

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

\int_{- \frac{1}{2}}^{\frac{3}{2}} x - cos (π x) d x

\int sin (x) cos (\frac{1}{2} x) d x

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