The equation of the tangent line to the curve y = 2x sin x at the poin

1.	The equation of the tangent line to the curve y = 2x sin x at the point \(\left(\frac \pi 2, \pi\right)\) is1. y = 2x + 2π2. y = 2x3. y = -2x + 2π4. y = -2x
Answer» Correct Answer - Option 2 : y = 2x Concept: The equation of tangent at point (x1 , y1) with slope m is given by \(\rm (y - y_1) = m (x - x_1)\) Calculations: Given curve is y = 2x sin x Taking derivative on both side, we get \(\rm \dfrac {dy}{dx}= 2x \;cos\;x + 2 \;sin\;x\) Put x = \(\rm \dfrac{\pi}{2}\) to find the equation of tangent at the point \(\left(\frac \pi 2, \pi\right)\). \(\rm \dfrac {dy}{dx}= 2 \dfrac {\pi}{2} \;cos\; \dfrac {\pi}{2} + 2 \;sin\; \dfrac {\pi}{2}\) \(\rm \dfrac {dy}{dx}= 2\) The equation of tangent at point (x₁, y₁) with slope m is given by \(\rm (y - y_1) = m (x - x_1)\) \(\rm (y - {\pi}) = 2 (x - \dfrac{\pi}{2})\) y = 2x Hence, the equation of the tangent line to the curve y = 2x sin x at the point \(\left(\frac \pi 2, \pi\right)\) is 2x.

The equation of the tangent line to the curve y = 2x sin x at the point \(\left(\frac \pi 2, \pi\right)\) is1. y = 2x + 2π2. y = 2x3. y = -2x + 2π4. y = -2x

Answer» Correct Answer - Option 2 : y = 2x

Concept:

The equation of tangent at point (x1 , y1) with slope m is given by

\(\rm (y - y_1) = m (x - x_1)\)

Calculations:

Given curve is y = 2x sin x

Taking derivative on both side, we get

\(\rm \dfrac {dy}{dx}= 2x \;cos\;x + 2 \;sin\;x\)

Put x = \(\rm \dfrac{\pi}{2}\) to find the equation of tangent at the point \(\left(\frac \pi 2, \pi\right)\).

\(\rm \dfrac {dy}{dx}= 2 \dfrac {\pi}{2} \;cos\; \dfrac {\pi}{2} + 2 \;sin\; \dfrac {\pi}{2}\)

\(\rm \dfrac {dy}{dx}= 2\)

The equation of tangent at point (x₁, y₁) with slope m is given by

\(\rm (y - y_1) = m (x - x_1)\)

\(\rm (y - {\pi}) = 2 (x - \dfrac{\pi}{2})\)

y = 2x

Hence, the equation of the tangent line to the curve y = 2x sin x at the point \(\left(\frac \pi 2, \pi\right)\) is 2x.

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