1)...... let A0 denotes the area bounded by f_{n}(x)=\left|\frac{sin(8nx)+cos(8nx)}{x} \right| , x -axis,y-axis and the line x=\pi /8
the prove that A_{n}>\frac{2\sqrt{2}}{\pi }\left[1+\frac{1}{2}.......\frac{1}{n} \right]
(n\epsilon N)
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2).....let set S contains infinite positive elements S:\left\{\theta _{1}+\theta _{2}+\theta _{3}+........ \right\}
such tat sum of all elements is \pi
show tat sin(\theta _{1})+sin(\theta _{2})+sin(\theta _{3})+.......\leq \pi
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3)....Let Tnn=1,2,3,4 represent four distinct positive real nos oder than unity such that each pair of the logarithm of Tn and the reciprocal of the logarithm denotes a point on a circle ,whose center lies on y axis.....find minimum value of T_{1}+T_{2}+T_{3}+T_{4}...(this one is easy)
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4).....let \vec{r} is a position vector of a variable point in cartesian OXY plane such that
\vec{r}.(10\hat{j}-8\hat{i}-\vec{r})=40 and p_{1}=max\left\{\left|\bar{r}+2\hat{i}-3\hat{j} \right|^{2} \right\}and p_{1}=min\left\{\left|\bar{r}+2\hat{i}-3\hat{j} \right|^{2} \right\}.
A tangent line is drawn to teh curve y=8/x2 at teh point A with absicca 2 if p1+p2 is even otherwise a normal line is drawn at teh same point.teh drawn line cuts the x-axis at a point B. find \bar{AB}.\bar{OB}
note a typo---(its P2=min{ })
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