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anonymous
 5 years ago
find the linearization of f(x) = 1/x at a=10
anonymous
 5 years ago
find the linearization of f(x) = 1/x at a=10

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The linearization of a function can be found using the following method: \[f(x) ≈ f(a)+f\prime(a)(xa)\] Where f(a) = 1/a f'(a) = d/dx(1/a) So, all we have to do is compute the derivative of f(x) and then we have everything we need to get the linearization. \[f(x) = 1/x = x^{1}\]\[f\prime(x)=x^{2}=1/x^{2}\] Now we just apply the rule to approximate the tangent line at x=a=3 so, \[f\prime(a) = 1/(3)^{2} = 1/9\]\[f(a) = 1/a = 1/3\] Therefore, the linear approximation of f(x) at a = 3 is \[f(x) ≈ 1/3  1/9(x  3)\] Now will you go on a date with me? :P

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha if your answer turns out to be correct? ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how would i use this to approximate 1/9.78 just plug that in for x?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yup, smart and beautiful.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0haha hardly smart if i'm on this thing but thank you
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