Q17 of 147 Page 183

If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2

: It is given that

y = (tan–1 x)2


On differentiating we get,






Again differentiating, we get,




So, (1+x2)2y2 + 2x(1+x2)y1 = 2


where,


Hence Proved


More from this chapter

All 147 →
15

If y = 500e7x + 600e–7x, show that .

 16

If ey (x + 1) = 1, show that=

1

Verify Rolle’s theorem for the function f (x) = x2 + 2x – 8, x ∈ [– 4, 2].

 2

Examine if Rolle’s theorem is applicable to any of the following functions. Can you say something about the converse of Rolle’s theorem from these examples?

(i) f (x) = [x] for x ∈ [5, 9]


(ii) f (x) = [x] for x ∈ [– 2, 2]


(iii) f (x) = x 2 – 1 for x ∈ [1, 2]