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

The limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi) is 1/4

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

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

\frac{1}{4}

Decimal

0.25

Solution steps

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

Apply L'Hopital's Rule

: x \to \frac{π}{4} lim (\frac{cos ( x - \frac{π}{4} )}{4})

= x \to \frac{π}{4} lim (\frac{cos ( x - \frac{π}{4} )}{4})

Plug in the value

x = \frac{π}{4}

= \frac{cos ( \frac{π}{4} - \frac{π}{4} )}{4}

cos (\frac{π}{4} - \frac{π}{4}) = 1

= \frac{1}{4}

x^{^{'}} + x = 0

\frac{1}{x} \frac{d y}{d x} = \frac{1}{x ^{2} + 1}

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x \to 0 lim (\frac{x e ^{x}}{sin ( x )})

n = 1 \sum \infty 1 (\frac{5}{6})^{n}

What is the limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi) ?
The limit as x approaches pi/4 of (sin(x-pi/4))/(4x-pi) is 1/4