Question

Find the equation of the normal to the curve $y=(1+x)+\left({\sin }^{2}x\right)$ at $x=0$.

Answer 1

$y=(1+x)+{\sin }^{1}x$

$\frac{dy}{dx}=1+2\sin x\cos x$ at $x=0$

$\frac{dy}{dx}=1$ slope of round $=-1$

At $x=0=1y=1$

$\therefore y-1=-1(x-0)=x+y=1$