Chapter 10: Problem 789
If \(\mathrm{y}=3 \mathrm{x}^{(3 / 2)}(\mathrm{x}-1)\) then \(|[\mathrm{dy} / \mathrm{d} \mathrm{x}]|_{(\mathrm{x}=1)}=\) (a) 6 (b) 3 (c) 1 (d) 0
Chapter 10: Problem 789
If \(\mathrm{y}=3 \mathrm{x}^{(3 / 2)}(\mathrm{x}-1)\) then \(|[\mathrm{dy} / \mathrm{d} \mathrm{x}]|_{(\mathrm{x}=1)}=\) (a) 6 (b) 3 (c) 1 (d) 0
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Get started for freeIf \(\mathrm{y}={ }^{\mathrm{x}} \sum_{\mathrm{r}=1} \tan ^{-1}\left[1 /\left(1+\mathrm{r}+\mathrm{r}^{2}\right)\right]\) then \((\mathrm{dy} / \mathrm{dx})=\) (a) \(\left[1 /\left(1+x^{2}\right)\right]\) (b) \(\left[1 /\left\\{1+(1+\mathrm{x})^{2}\right\\}\right]\) (c) 0 (d) \(\left[1 /\left\\{1-(\mathrm{x}+1)^{2}\right\\}\right]\)
If \(\mathrm{A}>0, \mathrm{~B}>0\) and \(\mathrm{A}+\mathrm{B}=(\pi / 3)\) than the maximum value of \(\tan \mathrm{A} \cdot \tan \mathrm{B}\) is (a) \((3 / 2)\) (b) \((1 / 3)\) (c) \((2 / 3)\) (d) 3
If \(\mathrm{e}^{\mathrm{y}}=\left(\mathrm{e}^{2} / \mathrm{x}^{2}\right)\) and \(\left[\left(\mathrm{d}^{2} \mathrm{y}\right) /\left(\mathrm{d} \mathrm{x}^{2}\right)\right]=\left(\mathrm{A} / \mathrm{x}^{2}\right)\) the \(\mathrm{A}=\) (a) \(-2\) (b) \((1 / 2)\) (c) 2 (d) \((1 / 3)\)
If \(\mathrm{f}(\mathrm{x})=|\mathrm{x}-1|\) any
\(\mathrm{g}(\mathrm{x})=\mathrm{f}\left(\mathrm{f}(\mathrm{f}(\mathrm{x}))\right.\)
the for \(\mathrm{x}>2, \mathrm{~g}^{\prime}(\mathrm{x})\) is equal to
(a) 1 for all \(x>2\)
(b) 1 for \(2
If \(\mathrm{y}=\mathrm{x} \tan (\mathrm{x} / 2)\) and \(\mathrm{A}(\mathrm{dy} / \mathrm{dx})-\mathrm{B}=\mathrm{x}\) then \((\mathrm{B} / \mathrm{A})=\) (a) \(\cot (\mathrm{x} / 2)\) (b) \(\tan (\mathrm{x} / 2)\) (c) \(\tan \mathrm{x}\) (d) \(\cot x\)
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