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
icon
Related questions
Question
100%

please do all parts step by step and i will make sure to upvote!! 

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.
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.
Expert Solution
steps

Step by step

Solved in 4 steps with 30 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,