Q21 of 45 Page 1

Finddy/dx if (x2 + y2)2 = xy.

OR


If y = 3 cos(log x) + 4 sin(log x), then show that x^2 d^2y/dx^2 + x dy/dx + y = 0

Given,


(x2 + y2)2 = xy


Differentiating both side w.r.t x









OR


Given,


y = 3cos(log x) + 4sin(log x)


Differentiating both side,





Differentiating both side again,






Hence, Proved!


More from this chapter

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19

Evaluate:

OR


Evaluate :

 20

Prove that the relation R on the set A = {1, 2, 3, 4, 5} given by R = {(a, b) :|a - b| is even }, is an equivalence relation.

 22

Find the equation of the tangent to the curve y = root 3x-2which is parallel to the line 4x - 2y + 5 = 0.

OR


Find the intervals in which the function f given by f (x) = x^3 + 1/x^3 , x not equal 0is


(i) increasing


(ii) decreasing.

 23

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r.

OR


A tank with rectangular base and rectangular sides, open at the top is to be constructed sothat its depth is 2 m and volume is 8 m3. If building of tank costs Rs. 70 per sq. metre for thebase and Rs. 45 per sq. metre for sides, what is the cost of least expensive tank?