Question

$x\stackrel{Lt}{\to }0[\frac{{\int }_0^x{\tan }^{2}t{\sec }^{2}tdt}{x^3}]=$

• A. 0
• B. 1
• C. 1/3
• D. 1/2

Answer 1

Answer: (C)

1/3

$l{t}_{x\to 0}\left[\frac{{\int }_0^x\left(ta{n}^{2}tse{c}^{2}t\right)dt}{x^3}\right]$
${}^0{/}_0$ form
So, $l{t}_{x\to 0}\frac{ta{n}^{2}xse{c}^{2}x}{3x^2}$
$l{t}_{x\to 0}\frac{ta{n}^{2}xse{c}^{2}x}{3x^2}$
$l{t}_{x\to 0}\frac{ta{n}^{2}x}{3x^2}$
${}^1{/}_3$