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(Solved): (a) Show that the equation xcosx=sinx has a solution in the interval a,b, with a=2024\pi ,b=a+(\pi ...
(a) Show that the equation
xcosx=sinxhas a solution in the interval
a,b, with
a=2024\pi ,b=a+(\pi )/(2)(b) Using a Taylor approximation, or otherwise, compute the limit:
\lim_(x->0)(tanx-x)/(x^(3)). (c) Prove that
|x^(2)arctanx-y^(2)arctany|<=(\pi +1)/(2)|x-y|for all
x,yin[0,1].
