(a) the volume of R using cylindrical coordinates with dV= r dz dr de where R: x≤ 1,0 ≤ y ≤ √1-x², 0≤z≤ √√4- (x² + y²). Draw the solid R.

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A:

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A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

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A:

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A: To find what element we get after operating the given elements.

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A: Leibnitz integral rule.

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A: The following differential equation is a Bernoulli equation:dydt+yt=y23 where y=ftBy making the…

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A: Use average concept

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A: Center of gravity is given.

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A: This question can be solved using the concept of area under curves.

Q: approaching

A: Please refer to the image below

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A: On solving this we will get

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A: First we draw the graph,

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Q: I can't understand your solution.

A: Let's solve given integral.

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A: Velocity and acceleration

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A:

Q: - 3x17 +10+10 - ) 4x19-3 b) (4x2 - 1)(7x3 + x)] + 100

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

Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: Evaluate the definite integral below. (Enter an exact answer.) Provide your answer below: S²4e³x-2…

A:

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A: This question is related to definite integration, we will solve it using given information.

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Q: II. Evaluate the following integrals. 3. 12-2² | dr

A:

Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

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A: Given problem:-

Q: Evaluate the following limits. 1. lim 1 cosh x x+0+ ln(x² + 1) 2. lim (tanx) (sin x-1) x+7+

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Q: The following differential equation is a Bernoulli equation: 2 dy + y3 where y = f(t) dt t By making…

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A:

Q: 2. The position of a particle moving horizontally is given by s(t) = t³ − 6t² + 9t + 4, where s is…

A: s(t)=t3-6t2+9t+4   position when instance change direction means v=0…

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A:

Q: I. Evaluate the following limits 2. lim (3 + x)² x → +∞o

A: Given

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A: A detailed solution is given below.

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A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: 9. A child is flying a kite with a 45-ft string at an angle of elevation of 50°. Which of the…

A: Let's find altitude of the kite in feet.