Let f : (–1, $$\infty $$) $$ \to $$ R be defined by f(0) = 1 and
f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$, x $$ \ne $$ 0. Then the function f :

The equation of the normal to the curve
y = (1+x)^2y + cos ²(sin^–1x) at x = 0 is :

Let P(h, k) be a point on the curve
y = x² + 7x + 2, nearest to the line, y = 3x – 3.
Then the equation of the normal to the curve at P is :

If the tangent to the curve y = x + sin y at a point
(a, b) is parallel to the line joining $$\left( {0,{3 \over 2}} \right)$$ and $$\left( {{1 \over 2},2} \right)$$, then :