What is the limit as x approaches 0 of (5xcot(3x))/(2sec(x)) ?

The limit as x approaches 0 of (5xcot(3x))/(2sec(x)) is 5/6

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limit as x approaches 0 of (5xcot(3x))/(2sec(x))

x \to 0 lim (\frac{5 x cot ( 3 x )}{2 sec ( x )})

\frac{5}{6}

Decimal Notation

0.83333 \dots

Solution steps

x \to 0 lim (\frac{5 x cot ( 3 x )}{2 sec ( x )})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= \frac{5}{2} \cdot x \to 0 lim (\frac{x cot ( 3 x )}{sec ( x )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{5}{2} \cdot \frac{lim _{x \to 0} ( x cot ( 3 x ) )}{lim _{x \to 0} ( sec ( x ) )}

x \to 0 lim (x cot (3 x)) = \frac{1}{3}

x \to 0 lim (sec (x)) = 1

= \frac{5}{2} \cdot \frac{\frac{1}{3}}{1}

Simplify

\frac{5}{2} \cdot \frac{\frac{1}{3}}{1} : \frac{5}{6}

= \frac{5}{6}

f (t) = 2 t sin (π t)

\int \frac{4 x ^{2} + 21 x + 54}{x ^{2} + 6 x + 13} d x

x \to 8 lim (6 x^{2} - 9 x + 1)

(\frac{3}{2})^{x}

y^{^{''}} - 4 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

What is the limit as x approaches 0 of (5xcot(3x))/(2sec(x)) ?
The limit as x approaches 0 of (5xcot(3x))/(2sec(x)) is 5/6