# 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 $$k+l+m+t+p$$

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