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Need solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Very short Answers Question 14 textbook solution.

Answers (1)

Answer : Required angle =\frac{\pi }{2}

Hint :

  1. If  m_{1}=m_{2}, they are parallel.
  2. If  m_{1} m_{2}=-1, they are perpendicular to each other.

Given :

Given that the curve,

y=e^{-x} \text { and } y=e^{x}

We have to find the angle between the given curves at the point of intersection.

Solution :


y=e^{-x}                                                                                 ....(i)

y=e^{x}                                                                                    .....(ii)

From (i) and (ii), we get

\begin{aligned} & e^{x}=e^{-x} \\ \Rightarrow & x=0 \end{aligned}

Substituting the value of x in equation (ii), we get


So, the point of intersection of the two curves is (0,1)

On differentiating (i) with respect to x, we get

\begin{aligned} &\frac{d y}{d x}=e^{x} \\ &m_{2}=\left(\frac{d y}{d x}\right)_{(0,1)}=1 \end{aligned}

\begin{aligned} & \therefore & & m_{1} m_{2} &=-1 \\ \text { Since } & & m_{1} m_{2} &=-1 \end{aligned},

Hence, they are perpendicular to each other.

Hence, the required angle =\frac{\pi }{2}


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