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

The limit as x approaches 0-of (4sin(x))/x is 4

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limit as x approaches 0-of (4sin(x))/x

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

4

Solution steps

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

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

= 4 \cdot x \to 0 - lim (\frac{sin ( x )}{x})

Apply L'Hopital's Rule

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

= 4 \cdot x \to 0 - lim (\frac{cos ( x )}{1})

Plug in the value

x = 0

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

Simplify

4 \cdot \frac{cos ( 0 )}{1} : 4

= 4

x \to 2 lim (\frac{1}{2} - 3 x)

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

x \to 4 lim (\frac{2 x}{x ^{2} - 16})

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

x \to 3 lim (ln (4 - x))

What is the limit as x approaches 0-of (4sin(x))/x ?
The limit as x approaches 0-of (4sin(x))/x is 4