Explanation Given: The function is y = 10 − x 2 2 + x 2 , where a = 1 , d x = 0.01 . Formula used: Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Calculation: The function is y = 10 − x 2 2 + x 2 . Differentiate the function with respect to x . y ′ = ( 2 + x 2 ) d d x ( 10 − x 2 ) − ( 10 − x 2 ) d d x ( 2 + x 2 ) ( 2 + x 2 ) 2 = ( 2 + x 2 ) ( − 2 x ) − ( 10 − x 2 ) ( 2 x ) (</

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 4.1, Problem 31E

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Estimate the value of Δy using differential.

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Chapter 4.1, Problem 30E

Chapter 4.1, Problem 32E

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For the following function f and real number a, a. find the slope of the tangent line mtan = f' (a), and b. find the equation of the tangent line to f at x = a. f(x)= 2 = a = 2 x2 a. Slope: b. Equation of tangent line: y

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Chapter 4 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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Estimate the value of Δ y using differential.

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