Differential and Integral Calculus by Feliciano and Uy, Exercise 1.3, Problem 16 Advertisements PROBLEM: Evaluate limx→0(1−cos2(x)1+cos(x)) \displaystyle \lim\limits_{x\to 0}\left(\frac{1-\cos^2\left(x\right)}{1+\cos\left(x\right)}\right)x→0lim(1+cos(x)1−cos2(x)) Advertisements SOLUTION: This problem can be solved using a direct substitution of x=0x=0x=0. That is limx→0(1−cos2x1+cosx)=1−cos2(0)1+cos(0)=1−11+1=0 (Answer)\begin{align*} \lim\limits_{x\to 0}\left(\frac{1-\cos^2 x }{1+\cos x }\right) & =\frac{1-\cos^2\left(0\right)}{1+\cos\left(0\right)} \\ \\ & =\frac{1-1}{1+1}\\ \\ & = 0 \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right) \end{align*}x→0lim(1+cosx1−cos2x)=1+cos(0)1−cos2(0)=1+11−1=0 (Answer) Advertisements Advertisements