What is the limit as x approaches 0 of (tan(9x))/(sin(4x)) ?

The limit as x approaches 0 of (tan(9x))/(sin(4x)) is 9/4

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limit as x approaches 0 of (tan(9x))/(sin(4x))

x \to 0 lim (\frac{tan ( 9 x )}{sin ( 4 x )})

\frac{9}{4}

Decimal

2.25

Solution steps

x \to 0 lim (\frac{tan ( 9 x )}{sin ( 4 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 (\frac{tan ( 9 x )}{sin ( 4 x )}) = \frac{9}{4}

x \to 0 + lim (\frac{tan ( 9 x )}{sin ( 4 x )}) = \frac{9}{4}

= \frac{9}{4}

What is the limit as x approaches 0 of (tan(9x))/(sin(4x)) ?
The limit as x approaches 0 of (tan(9x))/(sin(4x)) is 9/4