(c) Find y = f (x), the particular solution to the differential equation with the initial condition f (0) = 2.В I(d) For the particular solution y = f (x) found in part (c), find lim f (x).BI! Consider the differential equationd'y= 10 – 2y. Let y = f (x) be the particular solution to the differential equation with the initial condition f (0) = 2.(a) Write an equation for the line tangent to the graph of y = f (x) at x = 0. Use the tangent line to approximate f (0.5).I(b) Find the value ofat the point (0, 2). Is the graph of y = f (x) concave up or concave down at the point (0, 2) ? Givereason for your answer.I(c) Find y = f (x), the particular solution to the differential equation with the initial condition f (0) = 2.III!!!!!!

Answered: Consider the differential equation d'y…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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(c) Find y = f (x), the particular solution to the differential equation with the initial condition f (0) = 2.
В I
(d) For the particular solution y = f (x) found in part (c), find lim f (x).
B
I
!

Consider the differential equation
d'y
= 10 – 2y. Let y = f (x) be the particular solution to the differential equation with the initial condition f (0) = 2.
(a) Write an equation for the line tangent to the graph of y = f (x) at x = 0. Use the tangent line to approximate f (0.5).
I
(b) Find the value of
at the point (0, 2). Is the graph of y = f (x) concave up or concave down at the point (0, 2) ? Give
reason for your answer.
I
(c) Find y = f (x), the particular solution to the differential equation with the initial condition f (0) = 2.
I
II
!!!
!!!

Expert Solution

Step 1: Equation of the tangent to the given curve at x=0

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Approximation of f(0.5).

$L i n e a r A p p r o x i m a t i o n o f f (x) w h e n f (a) a n d f' (x = a) i s k n o w n . f (x) = f (a) + (x - a) f' (x = a) W h e n : x = 0.5, a = 0, f (0) = 2, f' (0) = 6 T h e a p p r o x i m a t e v a l u e o f f (0.5) = f (0) + (0.5 - 0) * f' (a) f (0.5) = 2 + (0.5 - 0) * 6 f (0.5) = 2 + 3 f (0.5) = 5$

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