Let's do trivia!
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The polar coordinates of \( (\sqrt{3}/2, 1/2) \) are
\( (1, \pi/6) \)
\( (1, \pi/3) \)
\( (1/2, \pi) \)
answer±
Use the formulae for polar coordinates.
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Velocity of \( r(t)=(1,t, t^2) \) is the following.
\( v(t)=(1,t, t^2) \)
\( v(t)=(0,1, 2t) \)
\( v(t)=(1,1, t) \)
none of above
answer±
Differentiate \( r(t)=(1,t, t^2) \) by components.
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Which vector field is gradient?
\( \langle 3,1,2 \rangle \)
\( \langle x,y,z+y \rangle \)
\( \langle yz, xz, xy \rangle \)
answer±
Apply a component test.
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Which plane below has a normal vector \( \langle 3,1,2 \rangle \)
3x+y+z+2
x^3+y+z^2=0
3x+y=-z
3xyz=2
answer±
Use the equation Ax+By+Cz=D.
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Write surface element for the surface \( z= x+y \).
\( \sqrt{3} \)
\( \sqrt{3}dxdy \)
\( \sqrt{3}dx \)
answer±
Use the formula \( \sqrt{f_x^2+f_y^2+1} \).
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Vector field \( \langle x, y \rangle \) is rotational.
FALSE
TRUE
answer±
Draw a picture of this vector field.
