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Problem 9.2.14. Show that each of the following is a continuous function at every point in its domain. (a) Any polynomial. (b) Any rational function. (A rational function is defined to be a ratio of polynomials.) (c) cos x. (d) The other trig functions: tan(x), cot(x), sec(a), and csc(x).

Problem 9.2.14. Show that each of the following is a continuous function at every point in its domain. (a) Any polynomial. (b) Any rational function. (A rational function is defined to be a ratio of polynomials.) (c) cos x. (d) The other trig functions: tan(x), cot(x), sec(a), and csc(x).

Advanced Engineering Mathematics
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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Problem 9.2.14 please 

Analytical math

 

12:22 M A personal.psu.edu/ecb! + continuous without having to rely on the definition. Problem 9.2.14. Show that each of the following is a continuous function at every point in its domain. (a) Any polynomial. (b) Any rational function. (A rational function is defined to be a ratio of polynomials.) Cos x. (d) The other trig functions: tan(x), cot(x), sec(r), and csc(x). Problem 9.2.15. What allows us to conclude that f(x) = sin (e*) is continuous at any point a without referring back to the definition of continuity? Theorem 9.2.1 can also be used to study the convergence of sequences. For example, since f(x) = e® is continuous at II II
Transcribed Image Text:12:22 M A personal.psu.edu/ecb! + continuous without having to rely on the definition. Problem 9.2.14. Show that each of the following is a continuous function at every point in its domain. (a) Any polynomial. (b) Any rational function. (A rational function is defined to be a ratio of polynomials.) Cos x. (d) The other trig functions: tan(x), cot(x), sec(r), and csc(x). Problem 9.2.15. What allows us to conclude that f(x) = sin (e*) is continuous at any point a without referring back to the definition of continuity? Theorem 9.2.1 can also be used to study the convergence of sequences. For example, since f(x) = e® is continuous at II II
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