Integral

[eager mountain]

Any help is needed

[jagged cipher]

$\lim_{x \to 0^+} \frac{\int_{0}^{x} \sqrt{t} cos t dt}{x^2}$ \\\
using l'hôpital rule by taking the derivative of both sides we get:\\\
$\frac{\frac{d}{dx} \int_{0}^{x} \sqrt{t} cos t dt}{\frac{d}{dx} x^2}$ \\\
simplify:\\\
$\frac{F'(x) - F'(0)}{2x}$

[tacit trellis]

せんく(It's Quantum)

[jagged cipher]

$\lim_{x \to 0^+}\frac{( \sqrt{x} cos x)-( \sqrt{0} cos 0 )}{2x}$ \\

[tacit trellis]

せんく(It's Quantum)