What is the limit as x approaches 0 of (4sin(3x))/(2tan(5x)) ?

The limit as x approaches 0 of (4sin(3x))/(2tan(5x)) is 6/5

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limit as x approaches 0 of (4sin(3x))/(2tan(5x))

x \to 0 lim (\frac{4 sin ( 3 x )}{2 tan ( 5 x )})

\frac{6}{5}

Decimal

1.2

Solution steps

x \to 0 lim (\frac{4 sin ( 3 x )}{2 tan ( 5 x )})

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

= \frac{4}{2} \cdot x \to 0 lim (\frac{sin ( 3 x )}{tan ( 5 x )})

Simplify

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

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{sec ^{2} ( 5 x ) \cdot 5})

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

Plug in the value

x = 0

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

Simplify

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

= \frac{6}{5}

x \to (\infty) lim (\frac{ln ( x )}{x})

x \to 1 lim (\frac{( x ^{2} )}{x - 1})

\int_{0}^{1} \frac{3 x ^{2}}{1 + x ^{3}} d x

x^{2} y^{^{''}} - 3 x y^{^{'}} + 5 y = 0

f (x) = 2 x^{2} - 9 x + 10, at x = 2

What is the limit as x approaches 0 of (4sin(3x))/(2tan(5x)) ?
The limit as x approaches 0 of (4sin(3x))/(2tan(5x)) is 6/5