`vecr=vecr_(0)+vecvt` and hence derive the relation `x=x_(0)+v_(x)t` and `y=y_(0)+v_(y)t`.

Find the derivative of sin (logx) (x>0) w.r.t.x

Area bounded by the relation [2x]+[y]=5, x , y >0 is___

Let f(x) be a real valued function satisfying the relation f(x/y) = f(x) - f(y) and lim_(x rarr 0) f(1+x)/x = 3. The area bounded by the curve y = f(x), y-axis and the line y = 3 is equal to

Find the area of the triangle formed by the lines y-x=0, x+y=0 and x-k=0.

The lines x-y-6=0, 4x-3y-20=0 and 6x+5y+8=0 are:

A curve passing through (2,3) and satisfying the differential equation int_(0)^(t)ty(t)d = x^(2)y(x), (x gt 0) is

Find a relation between x nd y if the points (x,y), (1,2) and (7,0) collinear.

Show that the function y=f(x) defined by the parametric equations x=e^(t)sin(t),y=e^(t).cos(t), satisfies the relation y''(x+y)^(2)=2(xy'-y)

Let y= int_(u(x))^(y(x)) f (t) dt, let us define (dy)/(dx) as (dy)/(dx)=v'(x) f (v(x)) - u' (x) f(u(x)) and the equation of the tangent at (a,b) and y-b=((dy)/(dx))(a,b) (x-a) . If y=int_(x^(2))^(x^(4)) (In t) dt , "then" lim_(x to 0^(+)) (dy)/(dx) is equal to