What is the limit as x approaches 0 of (tan(3x))/(sin(7x)) ?

The limit as x approaches 0 of (tan(3x))/(sin(7x)) is 3/7

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limit as x approaches 0 of (tan(3x))/(sin(7x))

x \to 0 lim (\frac{tan ( 3 x )}{sin ( 7 x )})

\frac{3}{7}

Decimal Notation

0.42857 \dots

Solution steps

x \to 0 lim (\frac{tan ( 3 x )}{sin ( 7 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 ( 3 x )}{sin ( 7 x )}) = \frac{3}{7}

x \to 0 + lim (\frac{tan ( 3 x )}{sin ( 7 x )}) = \frac{3}{7}

= \frac{3}{7}

\frac{\partial}{\partial y} (z^{3} - x y + yz + y^{3} - 2)

\int \frac{- 11 x}{( x ^{2} + 5 ) ^{2}} d x

\int \frac{1}{s ^{2} + 3 s + 6} d s

\frac{d}{d x} (tan^{- 1} (x))

2 x, x^{2}, 0, 2

What is the limit as x approaches 0 of (tan(3x))/(sin(7x)) ?
The limit as x approaches 0 of (tan(3x))/(sin(7x)) is 3/7