Explanation Given: The function is y = tan 2 x , where a = π 4 , d x = − 0.02 . 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 = tan 2 x . Differentiate the function with respect to x . y ′ = 2 tan x sec 2 x We know that, Δ y = d y . The formula of linear approximation is Δ y ≈ f ′ ( a ) Δ x

4th Edition

ISBN: 9781319379421

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 4.1, Problem 30E

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Estimate the value of Δy using differential.

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Chapter 4.1, Problem 29E

Chapter 4.1, Problem 31E

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A lighted candle burns outr according to the equation y'(t)=ky(t)_where y is the length (in inches) of the candle at any given time t (in hours). An 8-inch candle is reduced to half-length after 10 hours. Estimate the length of the candle after 12 hours. O 4.9 inches 3.5 inches O 5.6 inches O 2.8 inches

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Exercise 4: Let a be a positive number, solve the following IVP y (t) = 5(t – a), Note: This problem shows that the delta "function is the "derivative" of another function y(0) = 0. that we have studied this semester.

Chapter 4 Solutions

CALCULUS 4E (HC) W/ ACHIEVE ACCESS

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01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY

Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY

Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY

Estimate the value of Δ y using differential.

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Estimate the value of Δy using differential.

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