What is the limit as x approaches 0 of (tan(6x))/(sin(5x)) ?

The limit as x approaches 0 of (tan(6x))/(sin(5x)) is 6/5

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limit as x approaches 0 of (tan(6x))/(sin(5x))

x \to 0 lim (\frac{tan ( 6 x )}{sin ( 5 x )})

\frac{6}{5}

Solution steps

x \to 0 lim (\frac{tan ( 6 x )}{sin ( 5 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 ( 6 x )}{sin ( 5 x )}) = \frac{6}{5}

x \to 0 + lim (\frac{tan ( 6 x )}{sin ( 5 x )}) = \frac{6}{5}

= \frac{6}{5}

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

x \to 0 - lim (\frac{4}{5 x ^{\frac{1}{3}}})

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What is the limit as x approaches 0 of (tan(6x))/(sin(5x)) ?
The limit as x approaches 0 of (tan(6x))/(sin(5x)) is 6/5