Application of ...

Equation of the tangent at (1, -1) to the curve
$${ x }^{ 3 }-x{ y }^{ 2 }-4{ x }^{ 2 }-xy+5x+3y+1=0$$ is 

The angle between the curves $$y = \sin x$$ and $$y = \cos x$$ is 

If $$-4\le x\le 4$$, then critical points of $$f\left( x \right) ={ x }^{ 2 }-6\left| x \right| +4$$ are 

The tangent to the curve, $$y = xe^{x^2}$$ passing through the point $$(1, e)$$ also passes through the point:

The angle made by the tangent at any point on the curve $$x=a(t+\sin { t } \cos { t } ),y=a{ (1+\sin { t } ) }^{ 2 }$$ with x-axis is

The equation of the normal to the curve$$y=\left( 1+x \right) ^{ y }+{ sin }^{ -1 }\left( { sin }^{ 2 }x \right) at\quad x=0$$ is

If tangent at any point on the curve $${ y }^{ 2 }=1+{ x }^{ 2 }\ makes\ an\ angle\ \theta $$ with positive direction of the x-axis then

A particle moves along a line by $$s = \dfrac {1}{3} t^{3} - 3t^{2} + 8t + 5$$, it changes its direction when

Length of the normal to the curve at any point on the curve $$y=\dfrac { a\left( { e }^{ x/a }+{ e }^{ -x/a } \right)  }{ 2 } $$ varies as 

Function $$f(x)=\dfrac { \lambda sinx+6cosx }{ 2sinx+3cosx } $$ is monotonic increasing If