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

The limit as x approaches 0 of x/(sin(7x)) is 1/7

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

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

\frac{1}{7}

Decimal Notation

0.14285 \dots

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

cos (7 \cdot 0) \cdot 7 = 7

= \frac{1}{7}

y = 2 x^{2} - x + 1, (1, 2)

x \to 1 lim ((x^{2} + x)^{2})

f (t) = t e^{5 - 2 t}

\frac{d}{d a} (sin (a) cos (a))

(x^{2} + 2 x y) d x + x d y = 0

What is the limit as x approaches 0 of x/(sin(7x)) ?
The limit as x approaches 0 of x/(sin(7x)) is 1/7