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).
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.2: Applications Of Exponential Functions
Problem 47E
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Question
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0335de1d-d88b-4764-a43c-e2195c6bbbda%2Faf649190-49d0-4631-94d1-30a60995ca69%2F4hmgfai_processed.jpeg&w=3840&q=75)
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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