e. We can approximate, for small (real) values of x, sin (x) z x, cos(x) = 1-x?, and e*1+ x (you can use a Mathematica plot for each of these comparisons for small values of x as "proof"). What is a first order (i.e. linear) approximation of f(x) = tan(x)? Note: replacing, say, sin(x) by x for small values of x is very popular in physics, since it often simplifies the connected mathematics a lot

e. We can approximate, for small (real) values of x, sin (x) z x, cos(x) = 1-x?, and e*1+ x (you can use a Mathematica plot for each of these comparisons for small values of x as "proof"). What is a first order (i.e. linear) approximation of f(x) = tan(x)? Note: replacing, say, sin(x) by x for small values of x is very popular in physics, since it often simplifies the connected mathematics a lot

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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Question

We can approximate, for small (real) values of x, sin (x) z x, cos(x) = 1-x², and e* s 1+
е.
x (you can use a Mathematica plot for each of these comparisons for small values of x as
"proof"). What is a first order (i.e. linear) approximation off (x) = tan(x)?
Note: replacing, say, sin(x) by x for small values of x is very popular in physics, since it often
simplifies the connected mathematics a lot

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