What is the limit as x approaches+0 of sin(5x)csc(3x) ?

The limit as x approaches+0 of sin(5x)csc(3x) is 5/3

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limit as x approaches+0 of sin(5x)csc(3x)

x \to + 0 lim (sin (5 x) csc (3 x))

\frac{5}{3}

Decimal

1.66666 \dots

Solution steps

x \to 0 lim (sin (5 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 (sin (5 x) csc (3 x)) = \frac{5}{3}

x \to 0 + lim (sin (5 x) csc (3 x)) = \frac{5}{3}

= \frac{5}{3}

x \to - 2 lim (2 x^{3} + x^{2} - 4)

x \to - 2 lim (2 x^{2} - 8)

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

x \to + 0 lim (x \cdot ln (x))

x \to - 3 + lim (\frac{x ^{2} + 9}{x + 3})

What is the limit as x approaches+0 of sin(5x)csc(3x) ?
The limit as x approaches+0 of sin(5x)csc(3x) is 5/3