What is the limit as x approaches 0 of sin(5x)csc(9x) ?

The limit as x approaches 0 of sin(5x)csc(9x) is 5/9

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limit as x approaches 0 of sin(5x)csc(9x)

x \to 0 lim (sin (5 x) csc (9 x))

\frac{5}{9}

Decimal

0.55555 \dots

Solution steps

x \to 0 lim (sin (5 x) csc (9 x))

x \to a - lim f (x) = x \to a + lim f (x) = L

then

x \to a lim f (x) = L

x \to 0 - lim (sin (5 x) csc (9 x)) = \frac{5}{9}

x \to 0 + lim (sin (5 x) csc (9 x)) = \frac{5}{9}

= \frac{5}{9}

What is the limit as x approaches 0 of sin(5x)csc(9x) ?
The limit as x approaches 0 of sin(5x)csc(9x) is 5/9