What is the limit as x approaches pi of ((cos(x)+1))/((x-pi)^2) ?

The limit as x approaches pi of ((cos(x)+1))/((x-pi)^2) is 1/2

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limit as x approaches pi of ((cos(x)+1))/((x-pi)^2)

x \to π lim (\frac{( cos ( x ) + 1 )}{( x - π ) ^{2}})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

x \to π lim (\frac{cos ( x ) + 1}{( x - π ) ^{2}})

Apply L'Hopital's Rule

: x \to π lim (\frac{- sin ( x )}{2 ( x - π )})

= x \to π lim (\frac{- sin ( x )}{2 ( x - π )})

Apply L'Hopital's Rule

: x \to π lim (\frac{- cos ( x )}{2})

= x \to π lim (\frac{- cos ( x )}{2})

Plug in the value

x = π

= \frac{- cos ( π )}{2}

- cos (π) = 1

= \frac{1}{2}

\frac{s ^{2}}{s ^{4} + 2 s ^{2} + 1}

2 - 7 x

\int \frac{1}{x ^{2}} - \frac{3}{x ^{4}} d x

2 t e^{3 t} + 4 t^{2} e^{- 5 t}

\frac{d}{d x} (\frac{1}{2 x - 3})

What is the limit as x approaches pi of ((cos(x)+1))/((x-pi)^2) ?
The limit as x approaches pi of ((cos(x)+1))/((x-pi)^2) is 1/2