For JEE practice

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

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$-$ 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 $k+l+m+t+p$