Exercise 1, § 1

Functions of a Real Variable, V

Show that for $x$ real tending to $+\infty$ the function

f(x) = (x \cos^2 x + \sin^2 x) e^{x^2}

is monotone, but is neither comparable to

e^{x^2}

nor weakly comparable to

x^{1/2} e^{x^2}

Solution

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