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

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

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limit as x approaches 0 of (csc(7x))/(csc(3x))

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

\frac{3}{7}

Decimal

0.42857 \dots

Solution steps

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

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

= \frac{3}{7}

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

x \to 3 lim (\frac{1}{x ^{8.132}})

x \to 5 - lim (\frac{1}{5 - x})

x \to 0 lim (x ln (8 x))

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

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