Use a Taylor polynomial of the indicated degree to approximate the function at the given value of x. Round to seven decimal places.f(x) = 
and x = 10 to approximate 
; third degree at 8
A. 2 + 
(x - 8) - 
(x - 8)2 + 
(x - 8)3;
2.1824846
B. 2 + 
(x - 8) + 
(x - 8)2 + 
(x - 8)3;
2.1824846
C. 2 + 
(x - 8) - 
(x - 8)2 + 
(x - 8)3;
2.1547068
D. 2 + 
(x - 8) + 
(x - 8)2 + 
(x - 8)3;
2.1547068
Answer: C
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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. 
= y2 sin xy2; 
= 2[2y2 cos (xy2) - sin (xy2)] ; 
= 
= 2y[y2 cos (xy2) - sin (xy2)]
C. 
= -y4 cos xy2; 
= - 2x[2xy2 cos (xy2) + sin(xy2)]; 
= 
= - 2y[xy2 cos (xy2) + sin(xy2)];
D. 
= - y2 sin xy2; 
= 2y
; 
= 
= 2
Use the rules of exponents to simplify the expression. Write the answer with positive exponents. Assume that all variables represent positive real numbers.
A. y1/2
B. y
C. y9/8
D. 
Solve the logarithmic equation.log2x2 = log2(5x + 24)
A. {8, -3}
B. {8}
C. ?
D. 
Solve the problem.The profit (in millions of dollars) for Allied Manufacturing can be approximated by 
where x is the year 1989 ? x ? 2009. Approximate the average rate of change over a 5-year period. Round your answer to three decimal places when appropriate.
A. -6.735 million dollars B. -1.125 million dollars C. -0.315 million dollars D. -1.335 million dollars