Consider the following two expressions: f(x) =( e2x-(ex Cosx)2)/x2 and g(x)=(ex sin x/x)2, x!=0 (a) Show algebraically that f(x) = g(x) for all x != 0. [Hint: cos2 x + sin2 x=1 for all x].

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A: To find the non linear function by the given composition.

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A: Note:- As per your demand we solve question 14 and 15 for you  Given problems:-

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A: Given, f(x) = sin3x-2To evaluate:∫f(x) dx This can be done as follows:

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Note: As per our guidelines we are supposed to answer only the first three subparts. Kindly repost…

Q: Q14) [2x (1+x²) x-(1-x²) (1+x²) +CB)- 10 (1+x¹) (1+x²) (1+x²)" (1+x²)" 11 +00) +CD) 11 10 12 1.1…

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Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

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A: Asked questions are solved.

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Suppose f(x) =sin(3x- 2). Evaluate: A -3cos(3x- 2) +C B ® --cos( 3x – 2) +C © ;cos(3x – 2) + C D D…

A: Topic = Integration Correct option = B

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.