Theorem 1.6 (Taylor's series for a function of one variable) If f(x) is continuous and possesses continuous derivatives of order n in an interval that incules I = a, then in that interval (x) = F(a) + (x - a)f (a) + (x - a) (x - a)"-1 (n - 1)! -f"(a) + ... + 21 -rn-)(a) + R,(x). where R(x), the remainder term. can be expressed in the form R.(x) = ((). (x- a)" a < { < x. n!

Theorem 1.6 (Taylor's series for a function of one variable) If f(x) is continuous and possesses continuous derivatives of order n in an interval that incules I = a, then in that interval (x) = F(a) + (x - a)f (a) + (x - a) (x - a)"-1 (n - 1)! -f"(a) + ... + 21 -rn-)(a) + R,(x). where R(x), the remainder term. can be expressed in the form R.(x) = ((). (x- a)" a < { < x. n!

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

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