Find the limit of (1+cos(3x))/((x-pi)^2) as x approaches 0

 Exercise

$\lim_{x\to0}\left(\frac{1+\cos\left(3x\right)}{\left(x-\pi\right)^2}\right)$

 

Evaluate the limit $\lim_{x\to0}\left(\frac{1+\cos\left(3x\right)}{\left(x-\pi \right)^2}\right)$ by replacing all occurrences of $x$ by $0$

$\frac{1+\cos\left(3\cdot 0\right)}{\left(0-\pi \right)^2}$

 

Subtract the values $0$ and $-\pi $

$\frac{1+\cos\left(3\cdot 0\right)}{{\left(-\pi \right)}^2}$

 

Multiply $3$ times $0$

$\frac{1+\cos\left(0\right)}{{\left(-\pi \right)}^2}$

 

The cosine of $0$ equals $1$

$\frac{1+1}{{\left(-\pi \right)}^2}$

 

Add the values $1$ and $1$

$\frac{2}{{\left(-\pi \right)}^2}$

$\frac{2}{{\left(-\pi \right)}^2}$

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