AP EAMCET · Maths · Application of Derivatives
If the angle between the curves \(y=e^{2(1+x)-4}\) and \(x^2 y=1\) at the point \((1,1)\) is \(\theta\), then \(|\sin \theta|+|\cos \theta|=\)
- A \(7 / 5\)
- B \(3 / 5\)
- C \(8 / 7\)
- D \(6 / 5\)
Answer & Solution
Correct Answer
(A) \(7 / 5\)
Step-by-step Solution
Detailed explanation
Given the curves \(y=e^{2(1+x)-4}\) and \(x^2 y=1\) Now \(y=e^{2(1+x)-4} \Rightarrow y^{\prime}=2 e^{2 x-2}\) \(y^{\prime}(1)=2=m_1\) and \(x^2 y=1 \Rightarrow y=\frac{1}{x^2}\) \(\Rightarrow y^{\prime}=\frac{-2}{x^3} \Rightarrow y^{\prime}(1)=+2=m_2\) Since,…
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