What is the limit as x approaches 0 of tan(2x)csc(4x) ?

The limit as x approaches 0 of tan(2x)csc(4x) is 1/2

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limit as x approaches 0 of tan(2x)csc(4x)

x \to 0 lim (tan (2 x) csc (4 x))

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to 0 lim (tan (2 x) csc (4 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 (tan (2 x) csc (4 x)) = \frac{1}{2}

x \to 0 + lim (tan (2 x) csc (4 x)) = \frac{1}{2}

= \frac{1}{2}

y = x^{4} + 5 e^{x}, (0, 5)

\frac{d y}{d x} = π y + 12 e

x \to π lim (\frac{5 x}{3})

y = x, y = x

3^{x^{2} - 2 x + 1}

What is the limit as x approaches 0 of tan(2x)csc(4x) ?
The limit as x approaches 0 of tan(2x)csc(4x) is 1/2