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• 12 True or False : If $f(x)$ and $f^{-1}(x)$ intersect at an even number of points , all points lie on $y=x$
• 8 Find number of real roots using Sturm's method.
• 8 Is $ \lim_{n \to \infty} a_n ^{b_n} = e^{\lim_{n \to \infty}(a_n - 1)b_n}$ always true?
• 8 Prove that there is a $m \in \mathbb{R}$ so that $f(f(m)) = m$
• 7 Find the limit when $x = \pi / 6$
• 7 Indefinite integral of $\frac{\tan{(1+x^2)}}{1+x^2}$
• 6 Solving inequality involving floor function
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