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1
Vectors - Dot Product Properties
오답
(a) Show that \(\mathbf{i} \cdot \mathbf{j} = \mathbf{j} \cdot \mathbf{k} = \mathbf{k} \cdot \mathbf{i} = 0\).
(b) Show that \(\mathbf{i} \cdot \mathbf{i} = \mathbf{j} \cdot \mathbf{j} = \mathbf{k} \cdot \mathbf{k} = 1\).
내 답안
(미작성)
정답
해설 없음
2
Conic Sections - Shifted Ellipse
오답
Find the vertices and foci of the ellipse and sketch its graph.
\(9x^2 - 18x + 4y^2 = 27\)
내 답안
(미작성)
정답
해설 없음
3
MCQ
오답
If \(f(x) = \ln(\sqrt{x})\), then \(f''(x) =\)
A
\(-\dfrac{2}{x^2}\)
\(-\dfrac{1}{2 x^2}\)
정답
C
\(-\dfrac{1}{2 x}\)
D
\(-\dfrac{1}{2 x^{\dfrac{3}{2}}}\)
E
\(\dfrac{2}{x^2}\)
해설
\(f = \left(\dfrac{1}{2}\right) \ln x\). \(f' = 1/(2x)\). \(f'' = -1/(2 x^2)\).
4
Cylinders and Quadric Surfaces - Surfaces of Revolution
오답
Find an equation for the surface obtained by rotating the curve \(y = \sqrt{x}\) about the \(x\)-axis.
내 답안
(미작성)
정답
\(y^2 + z^2 = x\)
해설 없음
5
Comparison Test
오답
Determine whether the series converges or diverges.
\(\displaystyle\sum_{k=1}^{\infty} \dfrac{\sqrt[3]{k}}{\sqrt{k^3 + 4k + 3}}\)
내 답안
(미작성)
정답
Divergent
해설 없음