Question

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

• A. $b=\frac{\pi }{2}+a$
• B. $|a+b|=1$
• C. $|b-a|=1$
• D. $b=a$

Answer 1

The correct option is C $|b-a|=1$

${\begin{array}{c}\frac{dy}{dx}\end{array}|}_{p(a,b)}^c=\frac{2-\frac{3}{2}}{\frac{1}{2}-0}$

${\begin{array}{c}1+\text{cos b}=1\\ \text{cos b}=0\end{array}|}_{b=a+\sin b}^{p:(a,b)\text{lies on curve}}$

$b=a\pm 1$

$|b-a|=1$