A curve is described by y = x . Determine the approximate change in y if x varies from (π)/(3) to (π)/(3) + (π)/(100) .

Correct answer: B. 0.0157 Given y = x The approximate change in y is given by Δ y (dy)/(dx) Δ x Here, x = (π)/(3) and Δ x = (π)/(100) Differentiating y with respect to x , we get (dy)/(dx) = x At x = (π)/(3) , (dy)/(dx) = ((π)/(3)) = (1)/(2) Substituting the values, Δ y (1)/(2) × (π)/(100) = (π)/(200) Using π 3.14 , we get Δ y (3.14)/(200) = 0.0157

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Physics and Mathematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Physics and Mathematics

A curve is described by y = x . Determine the approximate change in...

A curve is described by

y = \sin x

. Determine the approximate change in

y

x

varies from

\dfrac{\pi}{3}

\dfrac{\pi}{3} + \dfrac{\pi}{100}

Options

A $0.0272$
B $0.0157$
C $0.0079$
D $0.0314$

Correct answer

B. $0.0157$

Step-by-step solution

Given

y = \sin x

The approximate change in

y

is given by

\Delta y \approx \dfrac{dy}{dx} \Delta x

Here,

x = \dfrac{\pi}{3}

and

\Delta x = \dfrac{\pi}{100}

Differentiating

y

with respect to

x

, we get

\dfrac{dy}{dx} = \cos x

x = \dfrac{\pi}{3}

\dfrac{dy}{dx} = \cos\left(\dfrac{\pi}{3}\right) = \dfrac{1}{2}

Substituting the values,

\Delta y \approx \dfrac{1}{2} \times \dfrac{\pi}{100} = \dfrac{\pi}{200}

Using

\pi \approx 3.14

, we get

\Delta y \approx \dfrac{3.14}{200} = 0.0157

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