anonymous
  • anonymous
Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sin 3x, x 0, = 0
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@satellite73 can u help please?
anonymous
  • anonymous
this is the same as "find the equation of the line tangent to the graph of \(y=\sin(3x)\) at \((0,0)\)"
anonymous
  • anonymous
take the derivative, replace \(x\) by 0 for the slope (you will get 3) and then use the point slope formula

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anonymous
  • anonymous
since the point is \((0,0)\) the equation of the line will be \(y=3x\)
anonymous
  • anonymous
ok so find the derivative of sin 3x right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok so i got 3cos(3x)
anonymous
  • anonymous
yes now evaluate at \(x=0\) to find your slope
anonymous
  • anonymous
ok i got 3
anonymous
  • anonymous
yes
anonymous
  • anonymous
that is the slope of your line
anonymous
  • anonymous
okay so now i have to use the point slop formula?
anonymous
  • anonymous
yes
anonymous
  • anonymous
but the point is \((0,0)\) so it is just \(y=3x\)
anonymous
  • anonymous
okay so what do i do next?
anonymous
  • anonymous
you are done
anonymous
  • anonymous
okay
anonymous
  • anonymous
linear approximation of f(x) at x=x0: \[f(x)=f(x_0)+(x-x_0)f'(x_0)\]
anonymous
  • anonymous
you can use this way too. (notice the resemblance to equation of line)

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