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The problem to use the intermediate value theorem to show that there is a root of the given equation in the specified interval.
sin(x)= x^2x, (1,2)
Can someone see if this is correct?
f(x) = sin(x)  x^2 + x, then f is continuous since sin(x) and x^2  x are continuous and their composition is also continuous. sin(x) = x^2  x which is equivalent to showing that f(x) = 0. f(1) = 0.841 and f(2) = 1.091, 0 s lying between f(1) and f(2). Since f is continuous, there is a c in (1,2) such that f(c) = 0
there is a root to the equation
sin(x) = x^2  x
 one year ago
 one year ago
The problem to use the intermediate value theorem to show that there is a root of the given equation in the specified interval. sin(x)= x^2x, (1,2) Can someone see if this is correct? f(x) = sin(x)  x^2 + x, then f is continuous since sin(x) and x^2  x are continuous and their composition is also continuous. sin(x) = x^2  x which is equivalent to showing that f(x) = 0. f(1) = 0.841 and f(2) = 1.091, 0 s lying between f(1) and f(2). Since f is continuous, there is a c in (1,2) such that f(c) = 0 there is a root to the equation sin(x) = x^2  x
 one year ago
 one year ago

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monroe17Best ResponseYou've already chosen the best response.1
@jim_thompson5910 can you check my work for me? :)
 one year ago

ivanmlernerBest ResponseYou've already chosen the best response.0
I'm sure it is right, but I'm not this jim.
 one year ago

monroe17Best ResponseYou've already chosen the best response.1
LOL! okay :) is there a specific format the answer needs to be in?
 one year ago

ZarkonBest ResponseYou've already chosen the best response.0
I wouldn't use 'their composition'
 one year ago

ZarkonBest ResponseYou've already chosen the best response.0
'their difference' would be better
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
You are correct, all polynomials are continuous Sine is continuous, so sin(x)  x^2 + x is continuous f(1) = 0.841 and f(2) = 1.091 So because of the sign change and because f(x) is continuous, there is a number c such that f(c) = 0 since f(1) < 0 < f(2)
 one year ago
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