(a) Find Maclaurin expansions for sin 2x, cos 2x and e³ up to and including the term in x³. I (b) Hence obtain an expansion for e³x cos +2x up to and including t 3 term in x³. (Leave all answers in exact form.)

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A: In this question, we want to prove that if a limit of a function exist then it must be unique.

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A: See the details solution in below

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A: Here the region of integration is bounded by y=x, y=1, x=0, x=1. Plotting the region we have:

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A: See this solution in below.

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A: To find cross product.

Q: Give a possible formula for the function below. Let A = (1, 21) and B = (2, 147). Use the general…

A: Given problem:- Give a possible formula for the function below. Let A = (1, 21) and B = (2, 147).…

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A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

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A: As we know that; The expression for the area of the triangle PQR is: A=12PQ→×PR→   Given: P=6,-3,-5,…

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A: ∫02 x2dx here we have to find equal to this. split the integral into two  use formula  ∫a  b f(x)dx…

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A: Find Volume of the set in 0&lt;=x&lt;=1, 0&lt;=y&lt;=1,&lt;=0z&lt;=5-x2-y2 .

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A: Given: limh→0lnx+h2+lnx2+1h

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A: See this solution in below

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A: Given: fx=e3x

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A: Here we have to use the concept of integration

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A: We need to find approximate area.

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A: A detailed solution is given below

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A: Given vectors:- a=-1,2,-4 b=2,-4,-8

Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

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A: To find the solution of given differential equation.