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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
 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
 one year ago

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

satellite73Best ResponseYou've already chosen the best response.2
this is the same as "find the equation of the line tangent to the graph of \(y=\sin(3x)\) at \((0,0)\)"
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
take the derivative, replace \(x\) by 0 for the slope (you will get 3) and then use the point slope formula
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
since the point is \((0,0)\) the equation of the line will be \(y=3x\)
 one year ago

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

satellite73Best ResponseYou've already chosen the best response.2
yes now evaluate at \(x=0\) to find your slope
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
that is the slope of your line
 one year ago

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

satellite73Best ResponseYou've already chosen the best response.2
but the point is \((0,0)\) so it is just \(y=3x\)
 one year ago

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

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

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