What is the limit as x approaches 0 of (x+cos(2x))^{csc(3x)} ?

The limit as x approaches 0 of (x+cos(2x))^{csc(3x)} is cube root of e

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limit as x approaches 0 of (x+cos(2x))^{csc(3x)}

x \to 0 lim ((x + cos (2 x))^{c s c (3 x)})

Decimal Notation

1.39561 \dots

Solution steps

x \to 0 lim ((x + cos (2 x))^{c s c (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 (cos (x - 1))

x \to 0 lim (\frac{x ^{2} - 3 x}{3 x})

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

x \to 2 - lim (2 x - 2)

x \to 0 lim ((1 + x)^{2})

What is the limit as x approaches 0 of (x+cos(2x))^{csc(3x)} ?
The limit as x approaches 0 of (x+cos(2x))^{csc(3x)} is cube root of e