JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the tangent to the curve \(y=x+\sin y\) at a point \((a, b)\) is parallel to the line joining \(\left(0, \frac{3}{2}\right)\) and \(\left(\frac{1}{2}, 2\right),\) then
- A \(b=a\)
- B \(\mathrm{b}=\frac{\pi}{2}+\mathrm{a}\)
- C \(|b-a|=1\)
- D \(|\mathrm{a}+\mathrm{b}|=1\)
Answer & Solution
Correct Answer
(C) \(|b-a|=1\)
Step-by-step Solution
Detailed explanation
Slope of tangent to the curve \(y=x+\sin y\) at \((a, b)\) is \(\frac{2-\frac{3}{2}}{\frac{1}{2}-0}=1\) \(\left.\Rightarrow \quad \frac{\mathrm{dy}}{\mathrm{dx}}\right]_{\mathrm{x}=\mathrm{a}}=1\) \(\frac{d y}{d x}=1+\cos y \cdot \frac{d y}{d x}(\) from equation of curve \()\)…
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