Use Theorems 14 to show that the function is continuous. (x) = x + sin x THEOREM

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Use Theorems 1–4 to show that the function is continuous.

THEOREM 1 Basic Laws of Continuity If f and g are continuous at x = c, then the following functions are also

THEOREM 2 Continuity of Polynomial and Rational Functions Let P and Q be polynomials. Then: P and Q are

THEOREM 3 Continuity of Some Basic Functions y = x/" is continuous on its domain for n a natural number. sin

THEOREM 4 Continuity of Composite Functions If g is continuous at x = c, and f is continuous at x = g(c),

ƒ(x) = x + sin x

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Oct 28, 2023 04:58 AM

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Use Theorems 14 to show that the function is continuous. (x) = x + sin x THEOREM

Question:

THEOREM 1 Basic Laws of Continuity If f and g are continuous at x = c, then the following functions are also continuous at x = C: (i) f + g and f-g (iii) fg (ii) kf for any constant k (iv) f/g if g(c) #0

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The polynomial function x is continuous by Theorem 2 and the ...View the full answer

Calculus

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