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1
Conic Sections - Parabola
Wrong
Find the vertex, focus, and directrix of the parabola and sketch its graph.
\(3x^2 + 8y = 0\)
My Answer
(No answer)
Correct Answer
No explanation
2
MCQ
Wrong
An equation for a tangent to the graph of \(y = \arcsin \dfrac{x}{2}\) at the origin is
\(x - 2 y = 0\)
Correct Answer
B
\(x - y = 0\)
C
\(x = 0\)
D
\(y = 0\)
E
\(\pi x - 2 y = 0\)
No explanation
3
Vectors - Representation
Wrong
Find a vector \(\mathbf{a}\) with representation given by the directed line segment \(\overrightarrow{A B}\). Draw \(\overrightarrow{A B}\) and the equivalent representation starting at the origin.
\(A(3, -1)\), \(B(2, 3)\)
My Answer
(No answer)
Correct Answer
\(\langle -1, 4 \rangle\)
No explanation
4
MCQ
Wrong
\(\displaystyle\int_{1}^{\infty} x/(1+x^2)^2 dx\)
A
\(-\dfrac{1}{2}\)
B
\(-\dfrac{1}{4}\)
\(\dfrac{1}{4}\)
Correct Answer
D
\(\dfrac{1}{2}\)
E
divergent
Explanation
\(u = 1 + x^2\), \(du = 2x dx\). \(\left(\dfrac{1}{2}\right) \displaystyle\int_{2}^{\infty} \dfrac{du}{u}^2 = -1/(2u)|_2^\infty = \dfrac{1}{4}\).
5
Conic Sections - Hyperbola
Wrong
Find the vertices, foci, and asymptotes of the hyperbola and sketch its graph.
\(y^2 - 16x^2 = 16\)
My Answer
(No answer)
Correct Answer
No explanation