Consider the function -3 f(x)=√1+z² (a) Find the linearization of the function f near z = 0. In other words, find the equation of the tangent line to the curve y = f(x) at the point where a = 0. 0 near = 0. Ljo(a)= (b) Use a calculator and part (a) to complete the following table with numerical expressions rounded to the sixth decimal place. To near x = 0 f(x0) L₁,0 (20) Eƒ.o(o) Rf.a (20)
Consider the function -3 f(x)=√1+z² (a) Find the linearization of the function f near z = 0. In other words, find the equation of the tangent line to the curve y = f(x) at the point where a = 0. 0 near = 0. Ljo(a)= (b) Use a calculator and part (a) to complete the following table with numerical expressions rounded to the sixth decimal place. To near x = 0 f(x0) L₁,0 (20) Eƒ.o(o) Rf.a (20)
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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Transcribed Image Text:2. Consider the function
0
√1+x
(a) Find the linearization of the function f near z = 0. In other words, find the equation of the
tangent line to the curve y = f(x) at the point where x = 0.
1
0.1
(b) Use a calculator and part (a) to complete the following table with numerical expressions rounded
to the sixth decimal place.
To near x = 0 f(x)
0.01
f(x) =
0.001
0.0001
-3x
Lfo(x)=
near x = 0.
Lƒ,o (To) Ef,o (ro)
Rf.a (To)
(c) Describe the behavior of the "relative error" column. You can think of x = 1 as "far away" from
x = 0. What would you expect of the relative error column in the first two rows of the table.
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