Apply Green's Theorem to evaluate the integral.
(y2 + 1) dx + (x2 + 2) dyC: The triangle bounded by x = 0, x + y = 2, y = 0
A. -24
B. 0
C. 32
D. 
Answer: B
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Find all the second order partial derivatives of the given function.f(x, y) = cos (xy2)
A. 
= - y2 sin xy2; 
= 2[ sin (xy2)- 2y2 cos (xy2)] ; 
= 
= 2y [sin (xy2)-y2 cos (xy2)]
B. 
= -y4 cos xy2; 
= - 2x[2xy2 cos (xy2) + sin(xy2)]; 
= 
=
- 2y[xy2 cos (xy2) + sin(xy2)];
C. 
= y2 sin xy2; 
= 2[2y2 cos (xy2) - sin (xy2)] ; 
= 
= 2y[y2 cos (xy2) - sin (xy2)]
D. 
= - y2 sin xy2; 
= 2y
; 
= 
= 2
Answer the question.How can the graph of f(x) = 
- 8 be obtained from the graph of y = 
?
A. Shift it horizontally 12 units to the left. Shift it 8 units down.
B. Shrink it horizontally by a factor of 
. Shift it 8 units down.
C. Shift it horizontally 12 units to the left. Shift it 8 units up.
D. Shift it horizontally 12 units to the right. Stretch it vertically by a factor of 8.
Provide an appropriate response.In a right triangle, the square of the length of the hypotenuse is equal to the ________.
A. area of the triangle B. square root of the sum of the other two side C. sum of the lengths of the other two sides D. sum of the squares of the other two sides
Provide an appropriate response.Find the value of 2x.
A. 36 B. 54 C. 108 D. 72