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anonymous
 3 years 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
anonymous
 3 years 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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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@satellite73 can u help please?

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes now evaluate at \(x=0\) to find your slope

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that is the slope of your line

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay so now i have to use the point slop formula?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0okay so what do i do next?

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

anonymous
 3 years 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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