What is the limit as x approaches 0 of (tan(9x))/(sin(6x)) ?

The limit as x approaches 0 of (tan(9x))/(sin(6x)) is 3/2

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limit as x approaches 0 of (tan(9x))/(sin(6x))

x \to 0 lim (\frac{tan ( 9 x )}{sin ( 6 x )})

\frac{3}{2}

Decimal

1.5

Solution steps

x \to 0 lim (\frac{tan ( 9 x )}{sin ( 6 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 ( 6 x )}) = \frac{3}{2}

x \to 0 + lim (\frac{tan ( 9 x )}{sin ( 6 x )}) = \frac{3}{2}

= \frac{3}{2}

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

x \to - 1 lim (- x^{5} + 6 x^{4} + 2)

x \to 3 lim (\frac{x ^{2} - 2}{x - 4})

x \to 0 lim (tan (\frac{3 π}{4}))

x \to - 3 lim (\frac{x + 5}{x ^{2} - 9})

What is the limit as x approaches 0 of (tan(9x))/(sin(6x)) ?
The limit as x approaches 0 of (tan(9x))/(sin(6x)) is 3/2