Area of Bounded Regions
A helicopter is flying along the curve given by $$y - x^{3/2} =7, (x \ge 0)$$. A solider positioned at the point $$\left(\dfrac{1}{2}, 7\right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is:
Area of Bounded Regions
A tangent to the curve, $$y=f(x)$$ at $$P(x, y)$$ meets $$x-$$axis at $$A$$ and $$y-$$axis at $$B$$. If $$AP:BP=1:3$$ and $$f(1)=1$$, then the curve also passes through the point.
Area of Bounded Regions
Let $$f(x)=\dfrac{\sin \pi X}{x^2},x>0$$
Let $$x_1
Area of Bounded Regions
If the normal to the curve $$y=f(x)$$ at the point $$(3,\,4)$$ make an angle $$\dfrac{3\pi}{4}$$ with the positive x-axis, then $$f'(3)$$ is
Area of Bounded Regions
The points at which the tangents to the curve $$y=x^3-12x+18$$ are parallel to x-axis are?
Area of Bounded Regions
Let $$y = f(x)$$ be a parabola, having its axis parallel to y-axis, which is touched by the line $$y =x$$ at $$x = 1$$, then
Area of Bounded Regions
Radius of the circle that passes through origin and touches the parabola $$y^2 = 4ax$$ at the point $$(a, 2a)$$ is
Area of Bounded Regions
The volume of the greatest cylinder which can be inscribed in a cone of height $$30cm$$ and semi-vertical angle $$30^0$$ is
Area of Bounded Regions
A rectangle is inscribed in an equilateral triangle of side length $$2a$$ units. The maximum area of this rectangle can be
Area of Bounded Regions
Tangents are drawn to $$x^2+y^2=16$$ from the point $$P(0,h)$$. These tangents meet the x-axis at $$A$$ and $$B$$. If the area of $$\Delta PAB$$ is minimum, then $$h=?$$