Question

$x\stackrel{Lt}{\to }0\left(\frac{x^4}{{\int }_0^{x^2}ta{n}^{-1}tdt}\right)=$

• A. 1
• B. 2
• C. 0
• D. 3

Answer 1

The correct option is B 2

$l{t}_{x\to 0}\frac{x^4}{{\int }_0^{x^2}ta{n}^{-1}tdt}$
${}^0{/}_0$ form $l{t}_{x\to 0}\frac{f_n}{g_n}l{t}_{x\to 0}\frac{f_n^{{}^{\prime }}}{g_n^{{}^{\prime }}}$
$l{t}_{x\to 0}\frac{4x^2}{\left(ta{n}^{-1}{x}^2\right)\left(2x\right)}=2l{t}_{x\to 0}\frac{x^2}{ta{n}^{-1}{x}^2}$
$=2$