f(x) = 2x + 1 g(x) = Vx + 4 y + 1 3. 2. 3.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Apply Newton’s Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the iterations until two successive approximations differ by less than 0.001.

f(x) = 2x + 1
g(x) =
Vx + 4
y
+
1
3.
2.
3.
Transcribed Image Text:f(x) = 2x + 1 g(x) = Vx + 4 y + 1 3. 2. 3.
Expert Solution
Step 1

Newton's method: It is an iterative technique used to find the approximation of the root of a real-valued

function using an initial approximation.

We have to use the Newton's method to find the approximation of x value at the point of intersection

of the functions fx and gx.

Step 2

Consider the initial approximation x0=0.5 which is the x-value at the point of intersection of the

functions fx and gx.

The point of intersection of the graphs of the functions fx and gx is computed by using the

equation 2x+1=x+4.

We can rewrite this equation as 2x+1-x+4=0. Let us define a function hx=2x+1-x+4.

This gives h'x=2-12x+4.

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