What is the limit as x approaches 0 of (sin(3x))/(sqrt(x+4)-2) ?

The limit as x approaches 0 of (sin(3x))/(sqrt(x+4)-2) is 12

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limit as x approaches 0 of (sin(3x))/(sqrt(x+4)-2)

x \to 0 lim (\frac{sin ( 3 x )}{x + 4 - 2})

12

Solution steps

x \to 0 lim (\frac{sin ( 3 x )}{x + 4 - 2})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{\frac{1}{2 x + 4}})

= x \to 0 lim (\frac{cos ( 3 x ) \cdot 3}{\frac{1}{2 x + 4}})

Plug in the value

x = 0

= \frac{cos ( 3 \cdot 0 ) \cdot 3}{\frac{1}{2 0 + 4}}

Simplify

\frac{cos ( 3 \cdot 0 ) \cdot 3}{\frac{1}{2 0 + 4}} : 12

= 12

\frac{d}{d x} (x^{4} - 5 x + 1)

\int_{0}^{3} 2 π (5 - x) (9 - x^{2}) d x

arcsin (x)

\frac{0.707}{s + 0.707}

\frac{d}{d x} (a \cdot cos (x) + b \cdot sin (x))

What is the limit as x approaches 0 of (sin(3x))/(sqrt(x+4)-2) ?
The limit as x approaches 0 of (sin(3x))/(sqrt(x+4)-2) is 12