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Explain solution for RD Sharma maths Class 12 Chapter 15 Tangents and Normals Exercise Multiple Choice Question, Question 33 maths textbook solution.

Answers (1)

Answer : (b) is the correct option

Hint : Equation of tangent y-y_{1}=m\left(x-x_{1}\right)

Given : y=e^{2 x}

Solution :

y=e^{2 x}                                                (1)

Differentiating (1) w.r.t x, we get

\begin{aligned} &\frac{d y}{d x}=2 e^{2 x} \\ &\left.\frac{d y}{d x}\right|_{x=0}=2 e^{0}=2 \end{aligned}

Equation of the tangent at the point (0, 1) and having the slope 2 is

\begin{aligned} &y-1=2(x-0) \\ &y-1=2 x \\ &y=2 x+1 \end{aligned}

Since it (2) meets in x-axis

\therefore y=0

Putting y=0 in (2)

0=2 x+1 \Rightarrow x=-\frac{1}{2}

\therefore The tangent meets at the point  P\left(\frac{-1}{2}, 0\right)

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