If cos(0) = 2, and 0 is in Quadrant II, then what is sin (:)? Give an exact answer, using radicals as needed. Rationalize the denominator and simplify your answer completely.

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A: Here we use the integration by parts.

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A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

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A: Simplify to get the standard form of first order linear differential equation.

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A: Consider the power series                 ∑n=1∞ an(x-a)n then series will convergent if x-a<R ,…

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Q: or false Let the domain of discourse be the set of all non negative even integers. Then, Vx,3y, (y2…

A: Solution of the problem as follows

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A: This is a problem related to number of regions in the sense number of interval for the given graph.…

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A: True.

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A: Given point P (2,3)

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A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

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Q: #12: use the definition of the derivative to calculate the derivative of f(x)=9x^2

A: Definition of derivative for a function f(x) is given by f'(x)=limh→0fx+h-fxh

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A: The given DE is: 2xy+x2dydx=3y2+2xy⇒x22yx+1dydx=3y2+2xy⇒2yx+1dydx=3yx2+2yx⇒dydx=3yx2+2yx2yx+1

Q: Find an equation of the plane that passes through the points (3, 2, 1), (2, 1, – 1), and (-1,3, 2).

A: Given:3,2,1, 2,1,-1   and -1,3,2