Find the degree 3 Taylor polynomial {eq}\displaystyle{ \rm T_3 (x) } {/eq} of function {eq}\displaystyle{ \rm f(x) = ( -3 x + 87 )^{\frac{ 5 }{ 4 }}\ at \ a = 2.} {/eq}
Question:
Find the degree 3 Taylor polynomial {eq}\displaystyle{ \rm T_3 (x) } {/eq} of function {eq}\displaystyle{ \rm f(x) = ( -3 x + 87 )^{\frac{ 5 }{ 4 }}\ at \ a = 2.} {/eq}
Taylor Polynomial:
We can construct a polynomial of any degree that approximates the value of a differentiable function close to a central point. To do so, we need to be able to take this function's derivative as many times as we want terms.
Answer and Explanation: 1
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View this answerTo find the third degree Taylor polynomial of this function, we need to calculate the following terms.
{eq}T_0 = f(a)\\ T_1 = f'(a)(x-a)\\ T_2 =...
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Chapter 8 / Lesson 10Read the Taylor series definition and learn about a special case of the Taylor series known as the Maclaurin series. See Taylor series examples and learn how to use the Taylor series formula.