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

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

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limit as x approaches infinity of sin(0)

x \to \infty lim (sin (0))

0

Solution steps

x \to \infty 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

n = 2 \sum \infty \frac{ln ( n )}{7 n}

n = 0 \sum \infty \frac{2 n}{n ^{2} + 1}

\frac{x}{x ^{2} + 4}

x x^{2} + 1

\frac{d}{d x} (\frac{x ^{2} + 1}{x})

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