Answer
$4$
Work Step by Step
$\lim_{\theta\to\pi/2}\frac{4tan^2\theta+tan\theta+1}{tan^2\theta+5}=\lim_{\theta\to\pi/2}\frac{4sin^2\theta+sin\theta cos\theta+cos^2\theta}{sin^2\theta+5cos^2\theta}=\lim_{\theta\to\pi/2}\frac{4(1)+(1) (0)+(0)}{1+5(0)}=4$
