What is the limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) ?

The limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) is 1/3

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limit as x approaches 1 of ((sin(pix)))/(sin(3pix))

x \to 1 lim (\frac{( sin ( π x ) )}{sin ( 3 π x )})

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

x \to 1 lim (\frac{sin ( π x )}{sin ( 3 π x )})

Apply L'Hopital's Rule

: x \to 1 lim (\frac{cos ( π x ) π}{cos ( 3 π x ) \cdot 3 π})

= x \to 1 lim (\frac{cos ( π x ) π}{cos ( 3 π x ) \cdot 3 π})

Plug in the value

x = 1

= \frac{cos ( π 1 ) π}{cos ( 3 π 1 ) \cdot 3 π}

Simplify

\frac{cos ( π 1 ) π}{cos ( 3 π 1 ) \cdot 3 π} : \frac{1}{3}

= \frac{1}{3}

e^{2 z}

4 sin^{2} (x)

\int 28 arctan (x) d x

\frac{d}{d x} (2 y e^{- x})

\frac{d y}{d x} = \frac{( 1 - x - y )}{x + y}

What is the limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) ?
The limit as x approaches 1 of ((sin(pix)))/(sin(3pix)) is 1/3