Application of ...

At what points of curve $$y = \dfrac{2}{3}x^{3}+\dfrac{1}{2}x^{2}$$, the tangent makes the equal with the axis?

The curve represented parametrically by the equations x = 2 in $$\cot t+1$$ and $$y=\tan t+\cot t$$ 

Let $$f(x)=\displaystyle \int e^x  (x-1)(x-2)dx$$. Then $$f$$ decreases in the interval

The number of tangents to the cure $$x^{3/2}+y^{3/2}=2a^{3/2}, a> 0$$, which are equally inclined to the axes, is 

The curve given by $$x + y = e^{xy}$$ has a tangent parallel to the y-axis at the point

If m is the slope of a tangent to the curve $$e^{y}=1+x^{2},$$ then 

If x=4 y = 14 is a normal to the curve $$y^{2}=ax^{3}-\beta $$ at (2,3) then the value of $$\alpha +\beta $$ is 

The angle between the tangent to the curves $$y = x^{2}$$ and $$x = y^{2}$$ at (1, 1) is 

At the point $$P(a, a^{n})$$ on the graph of $$y = x^{n}(n \epsilon  n)$$ in the first quadrant, a normal is drawn. the normal intersects the y-axis at the point (0, b) . if $$\underset{a\rightarrow b}{lim}b=\dfrac{1}{2}$$, then n equals

If a variable tangent to the curve $$x^{2}y=c^{3}$$ makes intercepts a, b on x-and y-axes, respectively, then the value of $$a^{2}b$$ is