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

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

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

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

\frac{6}{5}

Decimal Notation

1.2

Solution steps

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

= \frac{2}{5} \cdot x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{1})

Plug in the value

x = 0

= \frac{2}{5} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1}

Simplify

\frac{2}{5} \cdot \frac{cos ( 3 \cdot 0 ) \cdot 3}{1} : \frac{6}{5}

= \frac{6}{5}

\frac{\partial}{\partial x} (9 x^{7} cos (y^{4}))

f (x) = ln (64 sin^{2} (x))

y^{^{''}} - 3 y^{^{'}} - 4 y = e^{3 t}

y = \frac{x ^{3}}{2} + \frac{x ^{2}}{2} - 2 x, y = \frac{x ^{2}}{2}

f (x) = cos^{2} (3 x + 1)

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