Limit X Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cos4x}{x^2}$

Limit X Tends to Zero $\lim_{x\rightarrow 0}\frac{1 – cos4x}{x^2}$

$\lim_{x\rightarrow 0}\frac{1 – cos4x}{x^2}$

= $\lim_{x\rightarrow 0}\frac{\cos^22x + sin^22x – cos^22x + sin^22x}{x^2}$

=$ \lim_{x\rightarrow 0}\frac{2sin^22x}{x^2} $

= $\lim_{x\rightarrow 0}\frac{8sin^22x}{4x^2}$

= $8 \times \lim_{x\rightarrow 0}\frac{sin^22x}{4x^2} $

= $8 \times \left(\lim_{x\rightarrow 0}\frac{\sin 2x}{2x}\right)^2$

= $8 \times 1$

= 8