For this process we'll use the function f(x) = x² - 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I'm looking for help on the third bullet point starting with "For the same function..."
![For this process we'll use the function f(x) = x² -2.
2
. For a = 2, and the interval [2, 3], find each of the following without actually
calculating the equation of the tangent line, explaining how you do so, and illustrating
them on your graph (using screenshot annotation tools, for example, or some other
method). Zoom in enough to make sure each the quantities are shown clearly!
Ax
dr
Ay
dy
Now, find the equation of the tangent line at a = 2, and the equation of the secant
line for the interval [2, 3]. Add these two lines to your graph, and illustrate the
quantities Ac, dx, Ay, dy again. Explain the relationships between these quantities
and the tangent line and secant line.
For the same function, without calculating anything, sketch an illustration of the
Newton's Method process for finding the 1 and 2 approximations of the zero of the
function, using the seed value o = 2. (Draw in the lines that would produce the next
two approximations after this initial value.) Explain how each line produces the next
approximation.
Now use the Newton's Method formula to find ₁ and 2. How do they compare
to your illustration?
Because you already found the tangent line at = 2 in an earlier problem, use it
to verify the 1 value you got using the formula.
M
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Transcribed Image Text:For this process we'll use the function f(x) = x² -2.
2
. For a = 2, and the interval [2, 3], find each of the following without actually
calculating the equation of the tangent line, explaining how you do so, and illustrating
them on your graph (using screenshot annotation tools, for example, or some other
method). Zoom in enough to make sure each the quantities are shown clearly!
Ax
dr
Ay
dy
Now, find the equation of the tangent line at a = 2, and the equation of the secant
line for the interval [2, 3]. Add these two lines to your graph, and illustrate the
quantities Ac, dx, Ay, dy again. Explain the relationships between these quantities
and the tangent line and secant line.
For the same function, without calculating anything, sketch an illustration of the
Newton's Method process for finding the 1 and 2 approximations of the zero of the
function, using the seed value o = 2. (Draw in the lines that would produce the next
two approximations after this initial value.) Explain how each line produces the next
approximation.
Now use the Newton's Method formula to find ₁ and 2. How do they compare
to your illustration?
Because you already found the tangent line at = 2 in an earlier problem, use it
to verify the 1 value you got using the formula.
M
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