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 one year ago
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
 one year ago
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

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onegirl
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 can u help please?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2this is the same as "find the equation of the line tangent to the graph of \(y=\sin(3x)\) at \((0,0)\)"

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2take the derivative, replace \(x\) by 0 for the slope (you will get 3) and then use the point slope formula

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2since the point is \((0,0)\) the equation of the line will be \(y=3x\)

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0ok so find the derivative of sin 3x right?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2yes now evaluate at \(x=0\) to find your slope

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2that is the slope of your line

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0okay so now i have to use the point slop formula?

satellite73
 one year ago
Best ResponseYou've already chosen the best response.2but the point is \((0,0)\) so it is just \(y=3x\)

onegirl
 one year ago
Best ResponseYou've already chosen the best response.0okay so what do i do next?

electrokid
 one year ago
Best ResponseYou've already chosen the best response.0linear approximation of f(x) at x=x0: \[f(x)=f(x_0)+(xx_0)f'(x_0)\]

electrokid
 one year ago
Best ResponseYou've already chosen the best response.0you can use this way too. (notice the resemblance to equation of line)
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