Evaluate lim|x|/x or Findthesecondderivative y=ax+b/cx+d orIf fy=x^2yz+4xz^2finddel fy at P(1-2-1)

Evaluate lim|x|/x or Find the second derivative of y=ax+b/cx+d or If fy=x^2yz+4xz^2find del fy at P(1-2-1)
Find the volume of the solid generated by the revolution of the asteroid x^2/3+y^2/3=a^2/3 about x axis
Find the value of √1/2
Find all asymptote of the curve 2x^3-x^2y-2xy^2+y^3-4x^2+8xy-4x+1=0
If y=e^asin^-1 Show that (1-x^2)yn+2-(2n+1)xyn+1-(n^2+a^2)yn=0
Verify Green Theorem in the plane for (x^2-xy^3)dx+(y^2-2xy)dy where c is the square with vertices (0,0)(2,0)(2,2)(0,2)
Rolle's Theorem Lagrange's Mean Value Theorem And Cauchy Mean Value Theorem

Bsc 1st Semester Maths

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Test the continuity of the function at origin f(x)= {xe^1/x/1+e^1/x 0 if x=0Define convergent sequence/ Define continuous and differentiable functionsIfr=xi+yj+zkandr=|r| prove that div(r^nr)=n+3r^n or evaluate integral dxdy/1+x^2+y^2
Evaluatelimx^x/u=sin^-1x^2+y^2/x+yshowxdu/dx+ydu/dy=tanu/Findradiuscurvaturecurve y=e^xatpoint(0 1 )u=f(y+ax)+fy(y-ax)proved^2u/dx^2-a^2d^2u/dy^2=0OrIfu=sin^-1[x^2+y^2/x+y]thenshowxdu/dx+ydu/dy=tanu
Test the convergence of the series log2+log3/2+log4/3+... Or Show that lim|x-2|/x-2 does not exist
If z^3-xz-y=0 show that d^2z/dxdy=-{3z^2+x/(3z^2-x)^3}
Examine the continuity of the function defined by f(x)=-x^2 5x-4 4x^2-3x 3x+4 at the points x=012Find out right hand and left hand derivative at x=0 for the function f(x)= xtan^-11/x 0 for x=0If da/dt=r*a and d/dt = r*b then show that ddt(a*b) =r(a*b)Show that (axi+byj+czk)nds= 4/3pi(a+b+c) where s is the surface of sphere x^2+y^2+z^2=1A particle moves along the curve x=t^3+1 y=t^2 z=2t+5 where tis time.Then findthe accelerationat t=1
If four points withtheir positive vector a,b,c,d arecoplanarthenprove that [abc]= [bcd ]+[cad]+[abd]
Prove that the vector F=3y^4z^2i+4x^3z^2j-3x^2y^2k is solenoidal but not irrotational
Find the asymptote of the curve a=r(1-costheta)
Find the asymptote of curve y^3-x^2y-2xy^2+2x^3-7xy+3y^2+2x^2+2x+2y+1=0

Prove that the function f (x)=|x| is continuous at x=0 but not differentiable at x=0 Prove that curlfya=fycurla+gradfy*a Or Find our circular asymptote of the curve r=3theta/theta-1
If u=tan^-1 verify that d^2u/dxdy=d^2u/dydx
Show that the sequence Sn defined by Sn=1/n+1+1/n+2+...+1/n+n converges

Show that every convergent sequence is bounded but the converse need not be true||Mathematics||IMP

If x^xy^yz^z=c then prove that d^2z/dxdy=-(xlogex)^-1 when x=y=z
Bsc 1st Semester Physics Paper 2023-24 #SiddhartUniversity
Bsc 1st Semester Physics Paper 2023-24 #MJPRUniversityBsc 1st Semester Physics Paper 2023-24 #MJPRUniversity
Test the convergence the following series
Test the series whose nth term [(n^3+1)^1/3-n]
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