anonymous
  • anonymous
can somebody tell me what this is asking?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
The function for the tangent line is often called the first order approximation of 𝑓(π‘₯) at π‘₯=0, because it approximates the function with a straight line. The Taylor polynomial of degree 2 is often called the second order approximation of 𝑓(π‘₯) at π‘₯=0, because it approximates the function with a parabola. You can find higher order Taylor polynomials as well, to get third order approximations and so on. Show the following for your answers from (a) & (b): i. limπ‘₯β†’0𝑓 π‘₯ βˆ’πΏ π‘₯ π‘₯=0 but ii. limπ‘₯β†’0𝑓 π‘₯ βˆ’πΏ π‘₯ π‘₯2β‰ 0 (This means 𝐿(π‘₯) is only a first order approximation, not second order) iii. limπ‘₯β†’0𝑓 π‘₯ βˆ’π‘„ π‘₯ π‘₯2=0 (This means 𝑄(π‘₯) is a second order approximation.)

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