If f(x) = (1 − x)2 and g(x) = 8 − x, find f(g(x)) and g(f(x)) f(g(x)) = g(f(x)) =

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A: Follow the procedure given below.

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A: Evaluate arctan(sec ).

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A: Let's find.

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A: Given problem:- Use the cylindrical shell method to calculate the exact volume of the solid formed…

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A: Here, to rewrite the given integral: I=∫12022-f(x)2xdx...(1)

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A: We can solve this as follows:

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Q: If f'(x) =e*- 3 sin (x) und fco) = 4,what fcx)?

A: Topic = Integraion

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A: Please see the answer below.

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Q: Consider the following. u = 8i + 7j v = -7i +j+ 2k Find u x v. Determine if u x v is orthogonal to…

A: Here, the given vectors are: u=8i+7jv=-7i+j+2k

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Q: Let y=A cos x + B sinx is the solution of the differential equation

A: Follow the procedure given below.

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A: We can solve this as follows:

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A: Topic = Differenial equation Correct option = c

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A: I am attaching image so that you understand each and every step.

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Q: Find the devivatives of the following equation b Y= ln (x,4)-x fori CH/2)

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A: SOLUTION-

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Q: Simplify tan(arccot0).   undefined 0 pi/2

A: Topic = Trigonometry

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Q: By the series test: n=1 n´ +6n+3 6.

A: To determine whether the given series converges or diverges.∑n=1∞5n2+6n+3

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Q: Find the solutions of the system of inequalities by graphing: x + y > –1; 2x + y < -3

A: Given that: x + y &gt; -1 ; 2x + y &lt;= -3  We find the solution of the system of inequalities by…