Explanation Given: The given function is 4 cos x = x 2 . Calculation: The given function is, 4 cos x = x 2 − x 2 + 4 cos x = 0 ∴ f ( x ) = − x 2 + 4 cos x f ′ ( x ) = − 2 x − 4 sin x Substitute values of x and evaluate value of f ( x ) as shown below, x f ( x ) 0 4 1 1.161 2 − 5.665 Since, the value of f ( 1 ) is positive and the value of f ( 2 ) is negative, the required roots of the function lies between 1 and 2. The initial value can be plotted as , x ∘ = 1 + 2 2 x ∘ = 3 2 x ∘ = 1.5 The value of x ∘ is 1.5. First Iteration: f ( x ∘ ) = f ( 1.5 ) = − ( 1.5 ) 2 + 4 cos ( 1.5 ) f ( x ∘ ) = − 1.967 f ′ ( x ∘ ) = f ′ ( 1.5 ) = − 2 ( 1.5 ) − 4 sin ( 1.5 ) f ′ ( x ∘ ) = − 6.99 x 1 = x ∘ − f ( x ∘ ) f ′ ( x ∘ ) x 1 = 1.5 − − 1

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.7, Problem 19E

To determine

The solution of the given equation 4cosx=x2 up to 3 decimal places.

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Chapter 4.7, Problem 18E

Chapter 4.7, Problem 20E

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Let the region R be the area enclosed by the function f(x) = ex — 1, the horizontal line y = -4 and the vertical lines x = 0 and x = 3. Find the volume of the solid generated when the region R is revolved about the line y = -4. You may use a calculator and round to the nearest thousandth. 20 15 10 5 y I I I | I + -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 -5 I -10 -15 I + I I T I I + -20 I + -25 I I I -30 I 3.5 4 x

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Chapter 4 Solutions

CALCULUS (CLOTH)

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The solution of the given equation 4 cos x = x 2 up to 3 decimal places.

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Chapter 4 Solutions