1)find without l′hopital
lim_(x→0) ((2(√(x+1))−((x+1))^(1/3) −((x+1))^(1/4) )/x)
2) prove that the general solution for tbe differential equation
(1+y^2 )+(1+x^2 )((dy/dx))=0 is y=((k−x)/(1+kx)),k is a constant
then find the special solution if y=(2/(3 )) when x=1
A particle moving in a straight line OX has a
displacement x from O at time t where x satisfies
the equation (d^2 x/(dt^2 )) + 2(dx/dt) + 3x = 0
the damping factor for the motion is
[A] e^(−1)
[B] e^(−2t)
[C] e^(−3t)
[D] e^(−5t)
Which one of the following sets of
vectors is a basis for R^2
[A] { ((1),((−2)) ) , (((−3)),(6) )}
[B] { ((1),(1) ) , ((2),(2) )}
[C] { ((2),(1) ) , ((0),(1) )}
[D] { ((1),(2) ) , ((4),(8) ) }