- #1
cochemuacos
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Mean value theroem??
Show that x^2 = xsinx + cosx is true only for two values of x \in {R}
Intermediate value theorem
Mean value theorem (?)
I already know how to prove that there is al least one x \in [1,1.5] and another x \in [-1.5,-1] where the equation holds. The thing is that I'm not completely sure how to pove that they are unique, I have a geometric argument buy i feel it can be done using the mean value theorem.
Just for you to know, what i did to find out where the x's are, i took f(x) = x^2-xsinx-cosx and gave values to the function it turns out that f(1) < 0 and f(1.5) > 0 so there must be at leat one x \in [1,1.5] where f(x) = 0 But that's it, I ran out of ideas although i feel I'm really close.
Any ideas or advices will be appreiciated
Homework Statement
Show that x^2 = xsinx + cosx is true only for two values of x \in {R}
Homework Equations
Intermediate value theorem
Mean value theorem (?)
The Attempt at a Solution
I already know how to prove that there is al least one x \in [1,1.5] and another x \in [-1.5,-1] where the equation holds. The thing is that I'm not completely sure how to pove that they are unique, I have a geometric argument buy i feel it can be done using the mean value theorem.
Just for you to know, what i did to find out where the x's are, i took f(x) = x^2-xsinx-cosx and gave values to the function it turns out that f(1) < 0 and f(1.5) > 0 so there must be at leat one x \in [1,1.5] where f(x) = 0 But that's it, I ran out of ideas although i feel I'm really close.
Any ideas or advices will be appreiciated
