The number of points in (-infty, infty),for w | vedclass

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(C) Let $f(x) = x^2$ and $g(x) = x \sin x + \cos x$. We want to find the number of solutions to $f(x) = g(x)$.$f(0) = 0$ and $g(0) = 1$. Since $f(0) <

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$2$

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(C) Let $f(x) = x^2$ and $g(x) = x \sin x + \cos x$. We want to find the number of solutions to $f(x) = g(x)$.$f(0) = 0$ and $g(0) = 1$. Since $f(0) $f'(x) = 2x$ and $g'(x) = x \cos x$.For $x > 0$,$f'(x) = 2x$ and $g'(x) = x \cos x$. Since $\cos x \le 1$,$g'(x) \le x  0$. Thus,$f(x)$ grows faster than $g(x)$ for $x > 0$.Since $f(0)  0$.Since both $f(x)$ and $g(x)$ are even functions,there is also exactly one intersection point for $x Therefore,there are exactly $2$ points of intersection.

The number of points in $(-\infty, \infty)$,for which $x^2-x \sin x-\cos x=0$,is

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