Find the volume of the solid in R' bounded by y = x2, x = y?, z = x + y + 27, and z = 0.

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A: Given query is to find function is continuous or not.

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Q: The following series is an alternating serie

A: Since we are given with the multiple number of question and answered according to the guideline

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A: Topic:- inverse Laplace transform

Q: complete

A: Please refer to the image below

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A: We can solve as follows

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A: For f(x)=x+3 and g(x)=x+42, Our Aim is to find the formula forg∘fx and domain for g∘fx.

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A: 4.∫x2-1x+4dx

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Q: Find an eigenbasis and diagonalize. (Show the details.) 14.4 -11.2 10. -11.2 102.6.

A: Given :14.4-11.2-11.2102.6

Q: = csc() – y] dæ + ædy = 0 C CSC Dy = = cos-' (In z + C) O Ina + cos () = C O Inz (금) =C cos Oy = x…

A: Topic:- application of integration

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Q: S16 sin²x cos"x dx the solution is 2x 4 sin x cos x +2 sin x cos x +C 1 x- 2 sin x cos x + 4 sin x…

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A: Solution:

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Q: Consider the function g defined by 1 g(x, y) = cos (Tx VT) + log3 (x – y)" Determine

A: We can solve this as follows:

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Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

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Q: What is the significance of the fundamental theorems of calculus in the integration process?

A: This is a problem related to calculus. Based on the available concept we will answer the question.…

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Q: -olve for two cases csc² 20 cot 20 de irst case Using u = cot 20

A: Topic:-  integration

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Q: A ball is thrown vertically upward with a speed of 15 m/s. Determine the maximum height and the time…

A: Find maximum height and time to reach that's height

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A: Given; (s-20) /(s2-9).