Question

lim x->pi (1+cos^3x)/sin^2x (without L'hospital)

Answer 1

\(\large \lim \limits_{x \to \pi} \frac{1+\cos^3x}{\sin^2x} \)

\(\large \lim \limits_{x \to \pi} \frac{\sin^2x + \cos^2x+\cos^3x}{\sin^2x} \)

\(\large \lim \limits_{x \to \pi} \frac{\sin^2x }{\sin^2x} + \frac{\cos^2x+\cos^3x}{\sin^2x} \)

\(\large \lim \limits_{x \to \pi} 1 + \frac{\cos^2x(1+\cos x)}{1-\cos^2x} \)

\(\large \lim \limits_{x \to \pi} 1 + \frac{\cos^2x(1+\cos x)}{(1+\cos x)(1-\cos x)} \)

\(\large \lim \limits_{x \to \pi} 1 + \frac{\cos^2x}{(1-\cos x)} \)

Answer 2

take the limit..