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• 44 How can I justify this without determining the determinant?
• 13 Value of $\lim_{n\to \infty} \frac{1}{2^n} \sum_{k=1}^{2^n} \{\log_{2}k\}$
• 12 Solve: $\log_3(5(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})+2^{64})=?$
• 10 $ \begin{vmatrix} f(a) & g(a) & h(a) \\ f(b) & g(b) & h(b) \\ f'(c) & g'(c) & h'(c) \\ \end{vmatrix} =0 $
• 9 Justify: if $x\gt 0$, $\;\lim_{n\to\infty} \sqrt{n}\cdot{\overbrace{\sin\sin\cdots\sin}^{n\space\text{sines}}(x)}=\sqrt{3}$
• 9 find the value of $\int_{-a}^{a} \frac{f(x)} {1+e^x} dx $?
• 8 How to simplify or upperbound this summation?
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