Buds Public School, Dubai

Grade 12 Mathematics Holiday Assignment

  1. Examine the continuity of the function f(x)= .
  2. Differentiate log(sin (sec x)) with respect to x.
  3. Show that the function is strictly decreasing for .
  4. Evaluate.
  5. Differentiate cos x with respect to ex.
  6. Find the point on the curve y= where the rate of change of x- coordinate is equal to the rate of change of y co-ordinate
  7. Show that the function is decreasing in
  8. Evaluate :
  9. Differentiate the function y=tan-1 with respect to x.
  10. Find the equation of the tangent and normal to the curve 3x2-y =8 which passes through the point (4/3,0).
  11. Show that the function is not continuous at x = 0 .
  12. If , find the value of the derivative of with respect to x at the

point

  1. Using the differential, find the approximate value of
  1. If the rate of change of volume of a sphere is equal to the rate of change of its radius , find the

radius of the sphere .

  1. Find dx.
  2. Find the approximate value of .
  1. An edge of variable cube is increasing at the rate of 5 cm per second . How fast is the volume

decreasing when the side is 15 cm?

  1. Find dx.
  2. Evaluate :
  3. If y= A,prove that -(m+n) +mny=0.
  4. Evaluate :
  5. Prove that the curves = 4ax and xy =c2 cut at right angles if c4 =3a4 .
  6. If show that
  7. If
  8. Prove that
  9. Show that is an increasing function of x throughout its domain.
  10. Find a point on the curve , where the tangent is parallel to the chord joining (1,1) and
  11. (3,27).
  12. Find the intervals un which the function is

a) strictly increasing b) Strictly decreasing

  1. Evaluate :
  2. Evaluate :
  3. If
  4. If y = find
  5. Prove that is an increasing function in
  6. Find the point at which the tangent to the curve has its slope .
  7. Find the intervals un which the function is

a) strictly increasing b) Strictly decreasing

  1. Evaluate :
  2. Evaluate :
  3. Find 4x tan x dx.
  4. Evaluate dx.
  5. If , prove that .
  6. Differentiate the following with respect to x :
  7. If x= a(cos 2t + 2t sin2t) and y= a(sin 2t + 2t cos2t), then find
  8. Evaluate :
  9. Show that the semi- vertical angle of the cone of the maximum volume and of given slant

height is .

  1. Find the maximum area of an isosceles triangle inscribed in the ellipse with its

vertex at one end of the major axis .

  1. . Evaluate dx.
  2. 25. If
  3. Differentiate with respect to .
  4. If x=a(cos 2t + 2t sin2t) and y= a(sin 2t + 2t cos2t), then find
  5. Evaluate :
  6. . Prove that the volume of a largest cone that can be inscribed in a sphere of radius R of the

volume of the sphere.

  1. Prove that the semi –vertical angle at the right circular cone of given volume and least curved

surface area is .

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