Determine the interval, where f(x)=sin x - cos x, 0<x<2pie is strictly increasing or decreasing?

SHOW THAT THE SEMI-VERTICAL ANGLE OF RIGHT CIRCULAR CONE OF GIVEN SURFACE AREA AND MAX VOLUME IS SIN INVERSE(1/3).

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is sin^{-1} (1/3).

Sir please solve this as soon as possible..

show that the triangle of maximum area that can be inscribed in a given circle is an equilateral triangle

If straight line x cos(alpha) + y sin(alpha) = p touches the curve x^{2}/a^{2} + y^{2}/b^{2} = 1 , then prove that a^{2} cos^{2}(alpha) + b^{2} sin^{2}(alpha) = p^{2}.

Prove that the least perimeter of an isosceles triangle in which circle or radius r can be inscribed is 6root3 r

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum when the angle b/w them is pie/3.

An open box with a square base is to be made out of a given quantity of card board of area c^{2} square units. Show that the maximum volume of the box is c^{3}/ 6√3 cubic units.

water is dripping out from a conical funnel of semi vertical angle 45 at uniform rate of 2 cm^2/s (is its sure areea) through a tiny hole at vertical of the bottom wht is the rate of decrese of slant height when the slant height of water is 4cm

Water is leaking from a conical funnel at the rate of 5 cm3/sec.if the radius of the base of the funnel is 10cm and altitude is 20cm,Find the rate at which water level is dropping when it is 5cm from top..??

11a) Find maximum area of an isosceles triangle inscribed in the ellipse x^{2} / a^{2} + Y^{2 }/ b^{2} = 1 with its vertex at one end of the major axis.

Show that the semi-vertical angle of the cone fo masimum volume and of given slant height is tan inverse root 2

Show that the volume of greatest culinder that can be inscribed in a cone of height h and semi vertical angle alpha is 4/27 pi h cube tan square alpha

A man of height 2 metres walks at a uniform speed of 5 km/hr away from a lamp post which is 6 metres high.Please Find the rate at which the length of his shadow increases.

Find the angle between the parabolas y^{2} = 4ax & x^{2}= 4by at their point of intersection other than the origin ?

Determine the interval, where f(x)=sin x - cos x, 0<x<2pie is strictly increasing or decreasing?

SHOW THAT THE SEMI-VERTICAL ANGLE OF RIGHT CIRCULAR CONE OF GIVEN SURFACE AREA AND MAX VOLUME IS SIN INVERSE(1/3).

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is

sin.^{-1}(1/3)Sir please solve this as soon as possible..

show that the triangle of maximum area that can be inscribed in a given circle is an equilateral triangle

If straight line

x cos(alpha) + y sin(alpha) = ptouches the curvex, then prove that^{2}/a^{2}+ y^{2}/b^{2}= 1a.^{2}cos^{2}(alpha) + b^{2}sin^{2}(alpha) = p^{2}Prove that the least perimeter of an isosceles triangle in which circle or radius r can be inscribed is 6root3 r

If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum when the angle b/w them is pie/3.

An open box with a square base is to be made out of a given quantity of card board of area c^{2}square units. Show that the maximum volume of the box is c^{3}/ 6√3 cubic units.water is dripping out from a conical funnel of semi vertical angle 45 at uniform rate of 2 cm^2/s (is its sure areea) through a tiny hole at vertical of the bottom wht is the rate of decrese of slant height when the slant height of water is 4cm

Water is leaking from a conical funnel at the rate of 5 cm3/sec.if the radius of the base of the funnel is 10cm and altitude is 20cm,Find the rate at which water level is dropping when it is 5cm from top..??

11a) Find maximum area of an isosceles triangle inscribed in the ellipse

xwith its vertex at one end of the major axis.^{2}/ a^{2}+ Y^{2 }/ b^{2}= 1Show that the semi-vertical angle of the cone fo masimum volume and of given slant height is tan inverse root 2

Show that the volume of greatest culinder that can be inscribed in a cone of height h and semi vertical angle alpha is 4/27 pi h cube tan square alpha

A man of height 2 metres walks at a uniform speed of 5 km/hr away from a lamp post which is 6 metres high.Please Find the rate at which the length of his shadow increases.

Find the angle between the parabolas y

^{2}= 4ax & x^{2}= 4by at their point of intersection other than the origin ?