a) Determine if the geometric series 8n-1 90+1 n=1 is convergent or not, and find its sum if it is convergent. b) Find the partial sum S, in 3-digit accuracy.

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A: Please see the below picture for detailed solution.

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A: Here is the solution:

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A: Here is the answer:

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A: x+y=0  -----(1)x=-y x=y2+3y ------(2) for points of intersection y2+3y=-yy2+4y=0y(y+4)=0y=0,-4

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A: Given:      L-1ss-3s-4s-12 Taking Partial fractions of  ss-3s-4s-12

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A: In this question, We want to find the directional derivative in the given direction.

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A: Given data÷ r=2sinθ ,π2≤θ≤3π2   a) The graph on the interval is a circle and is given below

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A: To find out the rate of change in the direction of the given vector.

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A: The given function is: f(x,y)=4x2-2xy+2y3

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

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A: Please refer to the image below

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A: Starting from dashed graph let y=f(x)   Step-1 : Taking mirror reflection about  the horizontal…

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A: ∫02∫12x-3y2dydx=∫02x-7dx=-12

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Q: 10. Determine whether the series converges or diverges by using the integral test: Σnt n=1

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Q: Question 1 enclosed by Given the region D in R² y = 0, y = 1, x = 0, x = y² a. b. [ integral Sketch…

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A: We need to find volume and rate.

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A: A series ∑n=1∞un is said to be divergent if limn→∞un is nonzero. limn→∞1n3=0

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A: Given first term and common ratio put these in recursive formula