The slope of the tangent to the curve $y = \int_0^x \frac{1}{1+t^3} dt$ at the point where $x = 1$ is

The length of the subtangent to the curve $x^{2} y^{2}=a^{4}$ at $(-a, a)$ is

If the points of contact of the tangents drawn from $(0,0)$ to the curve $y=x^2+3x+4$ are $(\alpha, \beta)$ and $(\gamma, \delta)$,then $\beta+\delta=$

The tangent to the curve $y = 2x^2 - x + 1$ at a point $P$ is parallel to the line $y = 3x + 4$. The coordinates of $P$ are:

If the equation of the normal to the curve $y = \frac{x-a}{(x+b)(x-2)}$ at the point $(1, -3)$ is $x - 4y = 13$,then the value of $a+b$ is equal to $.......$.

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