COMEDK · Maths · 27. Application of Derivatives
The equation of normal to the curve \(y=(1+x)^{y}+\sin ^{-1}\left(\sin ^{2} x\right)\) at \(x=0\) is
- A \(x+y=1\)
- B \(x-y=1\)
- C \(x+y=-1\)
- D \(x-y=-1\)
Answer & Solution
Correct Answer
(A) \(x+y=1\)
Step-by-step Solution
Detailed explanation
Given the curve \(y = (1+x)^{y} + \sin^{-1}(\sin^{2}x)\). At \(x = 0\), \(y = (1+0)^{y} + \sin^{-1}(\sin^{2}0) = 1^{y} + 0 = 1\). Thus, the point of contact is \((0, 1)\). To find the slope of the tangent, differentiate the equation with respect to \(x\): Let \(u = (1+x)^{y}\).…
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