Find the point on the curve \( y=x^3-11x+5\) at which the tangent is y = x -11.

Find the area of the smaller region bounded by the ellipse\( \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\) and the line \( \dfrac{x}{a}+\dfrac{y}{b}=1\)

The area bounded by the y-axis, y = cos x and y = sin x when \( 0\leq x\leq \dfrac{\pi}{2}\)

A. \( 2(\sqrt{2}-1)\)

B.\(\sqrt{2}-1\)

C.\(\sqrt{2}+1\)

D.\(\sqrt{2}\)

The area of the circle x^{2} + y^{2} = 16 exterior to the parabola y^{2} = 6x is

A.\( \dfrac{4}{3}(4\pi-\sqrt{3})\)

B.\( \dfrac{4}{3}(4\pi+\sqrt{3})\)

C.\( \dfrac{4}{3}(8\pi-\sqrt{3})\)

D.\( \dfrac{4}{3}(4\pi+\sqrt{3})\)

The area bounded by the curve y = x |x| , x-axis and the ordinates x = –1 and x = 1 is given by [Hint: y = x^{2} if x > 0 and y = –x^{2} if x < 0]

A.0

B.\( \dfrac{1}{3}\)

C.\( \dfrac{2}{3}\)

D.\( \dfrac{4}{3}\)