Math Equation Testing

ax² + bx + c = 0

s = ut + ½ at<sup>2

∫cscn(x)dx=−1n−1cscn−2(x)cot(x)+n−2n−1∫cscn−2(x)dx</sup>

If $\Phi \left(x\right)={lim}_{n\to \infty }\frac{x^n-x^{-n}}{x^n+x^{-n}},0<x<1,ϵN$, then $\int \left(si{n}^{-1}x\right)\left(\Phi \right(x\left)\right)dx$ is equal to

$xsi{n}^{-1}\left(x\right)+\sqrt{1-x^2}+C$

$-\left(xsi{n}^{-1}\right(x)+\sqrt{1-x^2})$

$xsi{n}^{-1x+\sqrt{1-x^2}+C}$

None of these

A particle free to move along the x-axis has potential
energy given by U (x ) = k [1–exp(–x2)] for
-¥ £ x £ +¥,			where k is a positive constant of
appropriate dimensions. Then
(a)		at points away from the origin, the particle is in
		unstable equilibrium
(b)		for any finite nonzero value of x, there is a force
		directed away from the origin
(c)		if its total mechanical energy is k/2, it has its
		minimum kinetic energy at the origin.
(d)		for small displacements from x = 0, the motion
		is simple harmonic If f(x) = (sin2 x-1)n (2+ cos2x), then x = p / 2 is a point of (a) local maximum, if n is odd (b) local minimum, if n is odd (c) local maximum, if n is even (d) local minimum , if n is even The curve satisfying ydx – xdy + Inxdx = 0, (x>0) passing through (1, -1) is (a)  y + Inx + 1 = 0 (b) -y2 + Inx + 1 = 0 (c) y3 + (Inx)2 + 1 = 0 (d) none of these é 1 tan x ù , Then the value of |ATA–1| is If A = ê - tan x 1 ú ë û (a) cos4x (b) sec2x (c) –cos4x (d) 1 If three planes P 1 º 2x + y + z – 1 = 0, P 2 º X–y + z – 2 = 0 and p 3 º a x – y + 3z – 5 = 0 intersect each other at point P on XOY plane and at point Q on YOZ plane, where O is the origin then identify the

∫1dx=x+C$\int 1dx=x+C$

∫adx=ax+C$\int adx=ax+C$

∫xndx=xn+1n+1+C;n≠−1$\int x^{n}dx=\frac{x^{n+1}}{n+1}+C;n\ne -1$

∫sinxdx=–cosx+C$\int \sin xdx=–\cos x+C$

∫cosxdx=sinx+C$\int \cos xdx=\sin x+C$

∫sec2xdx=tanx+C$\int {\sec }^{2}xdx=\tan x+C$

∫csc2xdx=−cotx+C$\int {\csc }^{2}xdx=-\cot x+C$

∫secx(tanx)dx=secx+C$\int \sec x(\tan x)dx=\sec x+C$

∫cscx(cotx)dx=–cscx+C$\int \csc x(\cot x)dx=–\csc x+C$

∫1xdx=ln|x|+C$\int \frac{1}{x}dx=\ln |x|+C$

∫exdx=ex+C$\int e^{x}dx=e^x+C$

∫axdx=axlna+C;a>0,a≠1

$\int a^{x}dx=\frac{a^x}{\ln a}+C;a>0,a\ne 1$

∫11−x2−−−−−√dx=sin−1x+C$\int \frac{1}{\sqrt{1-x^2}}dx={\sin }^{-1}x+C$

<sup>∫

sinn(x)dx=−1nsinn−1(x)cos(x)+n−1n∫sinn−2(x)dx</sup>

Math Equation Testing pratik 4.9 of 5

ax 2  +  bx  +  c  = 0 s = ut + ½ at 2 ∫ csc n ( x ) d x = − 1 n − 1 csc n − 2 ( x ) cot ( x ) + n − 2 n − 1 ∫ csc n − 2 ( x ) d x ...