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Syllabus

dx / 4x

^{2}- 4x + 2^{2}-4x-5/ x-1 dx^{x }dxQ. Use Rolle's theorem to prove that the equation $a{x}^{2}+bx=\frac{a}{3}+\frac{b}{2}$ has a root between 0 and 1.

(Given a, b $\in $ R)

The least positive integer n for which √(n+1) – √(n-1) < 0.2 is

Solve this :$2.\mathrm{Find}\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{critical}\mathrm{points}\mathrm{for}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{max}(\mathrm{sinx},\mathrm{cosx})\mathrm{for}\mathrm{x}\in (0,2\mathrm{\pi}).$

Q. Evaluate : ${\int}_{0}^{\raisebox{1ex}{$\mathrm{\pi}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}\mathrm{cos}2xdx$

^{1/2 }PLeAsE InTeGrAtE tHe cHeCkEd sUmS WiTh ReSpEcT tO"x"

Put tan

x = t$\int (2x+1{)}^{2}dx$

Ans: 4.

${\int}_{0}^{\pi /4}{\mathrm{cos}}^{2}xdx?\phantom{\rule{0ex}{0ex}}A)\frac{\pi -2}{2}\phantom{\rule{0ex}{0ex}}B)\frac{\pi +2}{8}\phantom{\rule{0ex}{0ex}}C)\frac{\pi -2}{4}\phantom{\rule{0ex}{0ex}}D)\frac{\pi +2}{4}$

Ans: opt 3.

Help asap

Ans :4

Getting opt 1

How do I solve such problems where powers have been added to trigo functions?!

Q.12]. ${\left(x-y\right)}^{2}{a}^{2}+2\left(x-y\right)\left(x+y\right)ab+{b}^{2}{\left(x+y\right)}^{2}$

Ans: BC. Is there any catch in option D?

(1) Zero

(2) $\frac{T}{\mathrm{\pi}}$

(3) $\frac{2T}{\mathrm{\pi}}$

(4) $\frac{2}{\mathrm{\pi}}$