Question

Find the equations of the normal to the curve y = (1 + x)^y + sin^–1(sin²x) at x = 0. 

Answer 1

Given curve is y = (1 + x) y + sin^–1(sin²x)

y = e^ylog(1+x) + sin^–1(sin²x)

when x = 0, then y = 1.

So, the point is (0, 1)

(dy/dx)_(0,1) = 1

So, slope of the normal = – 1

Hence, the equation of the normal is

y – 1 = – 1(x – 0) = –x

⇒ x + y = 1