Question: Use Theorems 14 to show that the function is continuous. (x) = x + sin x THEOREM 1 Basic Laws of Continuity If f and

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

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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