What is the limit as x approaches 0 of (7x)/(sin(x)) ?

The limit as x approaches 0 of (7x)/(sin(x)) is 7

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limit as x approaches 0 of (7x)/(sin(x))

x \to 0 lim (\frac{7 x}{sin ( x )})

7

Solution steps

x \to 0 lim (\frac{7 x}{sin ( x )})

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

= 7 \cdot x \to 0 lim (\frac{x}{sin ( x )})

Apply L'Hopital's Rule

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

= 7 \cdot x \to 0 lim (\frac{1}{cos ( x )})

Plug in the value

x = 0

= 7 \cdot \frac{1}{cos ( 0 )}

Simplify

7 \cdot \frac{1}{cos ( 0 )} : 7

= 7

f (x) = 5 x + 6

\int cos (2 x) d x

\frac{d P}{d t} = - \frac{1}{2} P + t

\frac{d y}{d x} = x^{2} sec (y)

\frac{d}{d x} (3 x \cdot e^{2 x})

What is the limit as x approaches 0 of (7x)/(sin(x)) ?
The limit as x approaches 0 of (7x)/(sin(x)) is 7