What is the limit as x approaches infinity of ((2sin(3x)))/(5x) ?

The limit as x approaches infinity of ((2sin(3x)))/(5x) is 0

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limit as x approaches infinity of ((2sin(3x)))/(5x)

x \to \infty lim (\frac{( 2 sin ( 3 x ) )}{5 x})

0

Solution steps

x \to \infty lim (\frac{2 sin ( 3 x )}{5 x})

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

= \frac{2}{5} \cdot x \to \infty lim (\frac{sin ( 3 x )}{x})

Apply the Squeeze Theorem:

0

= \frac{2}{5} \cdot 0

Simplify

= 0

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

x \to - 3 lim (x^{2} + 5 x + 6)

x \to \infty lim (- x^{0})

x \to 0 lim (e^{1 - x})

x \to \infty lim (- 2 x + 5)

What is the limit as x approaches infinity of ((2sin(3x)))/(5x) ?
The limit as x approaches infinity of ((2sin(3x)))/(5x) is 0