# For JEE practice

**Calculus**Level 5

Note: We likely should make the assumption that \(n\) is restricted to being an integer.

\(-\) If the number of points of discontinuity is \(k\) for

\(\large{\displaystyle \lim_{n\to \infty} \dfrac{\ln(1+x)-x^{2n}\sin x}{1+x^{2n}}}\)

\(-\) If the area bounded by \(xy=2(\sqrt{2}-x)\) is \(l~sq~units\)

\(-\) If \(\displaystyle \int_{0}^{\pi} |\sin(2013x)|+|\sin(2014x)|+|\sin(2015x)|.dx=m\)

\(-\) if \(\displaystyle \lim_{n\to \infty} n \sin (2 \pi \sqrt{1+n^{2}})=t\)

\(-\) If number of solution of \(\sin^{4} \pi x=\ln x\) is\are \(p\)

Find \(k+l+m+t+p\)