Question

exercicios de limites resolvidos? me ajudeeem por favor!

Answer 1

Bom lim x^2-4/x+2= 0/0 x=>2 lim (x+2)(x-2)/x+2 x=>2 lim x-2 x=>2 lim 2-2 x=>2 2-2=0

Answer 2

$\displaystyle \lim_{x\to0}\frac{\sec(x)-1}{x^2}\implies \lim_{x\to0}\frac{\sec(x)-1}{x^2}\cdot\frac{\sec(x)+1}{\sec(x)+1}=\lim_{x\to0}\frac{\sec^2(x)-1}{x^2\cdot(\sec(x)+1)}\\\\\implies 1+\tan^2(x)=\sec^2(x)\implies \tan^2(x)=\sec^2(x)-1\implies \\\\\lim_{x\to0}=\frac{\tan^2(x)}{x^2\cdot(\sec(x)+1)}\implies \left(\lim_{x\to0}\frac{\tan^2(x)}{x^2}=1\right)\implies \lim_{x\to0}\sec(x)=1\\\\\lim_{x\to0}\frac{\tan^2(x)}{x^2}\cdot\frac{1}{\sec(x)+1}=1\cdot\frac{1}{1+1}=\boxed{\frac{1}{2}}$