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

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

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

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

4

Solution steps

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

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

= 4

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

\int e^{c o s (38 t)} sin (38 t) d t

\frac{d}{d x} (x^{2} + 8 x + 7)

y = x, y = 2 x - 15, y = 0

5 \frac{d v}{d t} = 49.05 - 50 v

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