Determine whether F is conservative. If so, find a function f such that F = ?f.


Mathematics

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Use reduction formulas to evaluate the integral.

A. 2 sin 4x -  cos3 4x + C
B. 2 sin 4x +  sin3 4x + C
C. 8 sin 4x -  sin3 4x + C
D. 2 sin 4x -  sin3 4x + C

Mathematics

If the 14th term of an arithmetic sequence is 67 and the 9th term is 42, find the 40th term. ? 

A. 195 B. 197 C. 200 D. 202 E. none of the above

Mathematics

Solve the equation.log (2 + x) - log (x - 2) = log 5

A. ?
B. - 3
C.
D. 3

Mathematics

The function  represents the value of the U.S. dollar in Indian rupees as a function of the time t in days. Find the average rates of change of  over the time intervals

data-wiris-created="true" src="https://sciemce.com/media/3/ppg__cognero__3.5_Derivatives_Numerical_and_Graphical_Viewpoints__media__021ddde2-b1ad-410e-b0b8-5762e2db41f7.PNG" style="vertical-align:middle;" />, where t is as indicated and , , , and  days. Hence, estimate (using ) the instantaneous rate of change of  at time .
?
Select your answer rounded to the nearest whole number.
?

A. 63
B. 69
C. 64
D. 67
E. 68

Mathematics