What is the limit as x approaches 0 of (tan(12x))/(sin(4x)) ?

The limit as x approaches 0 of (tan(12x))/(sin(4x)) is 3

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limit as x approaches 0 of (tan(12x))/(sin(4x))

x \to 0 lim (\frac{tan ( 12 x )}{sin ( 4 x )})

3

Solution steps

x \to 0 lim (\frac{tan ( 12 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 ( 12 x )}{sin ( 4 x )}) = 3

x \to 0 + lim (\frac{tan ( 12 x )}{sin ( 4 x )}) = 3

= 3

\frac{\partial}{\partial x} (y e^{x} - x^{2} y^{- 3})

t an g e n t y = \frac{4 x}{x ^{2} + 1}, (0, 0)

x \to - 1 lim (x^{2} - 2 x + 3)

\frac{d}{d x} (- \frac{cos ^{4} ( x )}{4})

\int 1 - e^{- 2 x} d x

What is the limit as x approaches 0 of (tan(12x))/(sin(4x)) ?
The limit as x approaches 0 of (tan(12x))/(sin(4x)) is 3