chris215
  • chris215
Which of the following is the best linear approximation for f(x) = sin(x) near x = π seconds? y = -x + π - 1 y = -1 y = -x + π y = -x - π
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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zepdrix
  • zepdrix
Hmm I don't think you need to do anything fancy here. Just think about the `actual value` of sin(x) at x=pi, and see which options gets you closest to that value.
zepdrix
  • zepdrix
\[\large\rm \sin(\pi)=?\]
anonymous
  • anonymous
@zepdrix is right. TIP: It's equally beneficial to glance at a sine wave on a graph.

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anonymous
  • anonymous
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anonymous
  • anonymous
For a more systematic way (assuming you know calculus), the linear approximation of a function at a point is: \(L = f(x_{0}) + f'(x_{0})(x-x_{0})\) Then just throw everything into that formula. \(\large \sin(\pi) = ?\) \(\large \frac{d}{dx}\sin(x) \rvert_{x=\pi} = ?\)
chris215
  • chris215
-1?
zepdrix
  • zepdrix
\(\large\rm \sin(\pi)\ne-1\)
chris215
  • chris215
ok so does that mean the answer is y=-1?

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