Find the radius of convergence, R, of the series. Σ. n = 1 R = 9nxn n4 Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =

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Q: b) use Polar Coordinates to compute SS. (x+y) JA the first quadrant where R is the region in between…

A: R is the region between the circles of radius 1 and 3 in first quadrant.

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A: Here water bottle is at height of 80 m initially. We will use equation of motion.

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Q: 2. Compute the derivative with respect to x of each function below using differentiation rules. (a)…

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Q: 2. An oil field is estimated to produce oil at a rate of R(t) thousand barrels per month t months…

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Q: Graph f(8)= -3sin(26)- 1 where 0 ≤ 0≤ 1. State the period and amplitude of the function.

A: Consider the function .The amplitude is .The period is .

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Q: The number of visitors P to a website in a given week over a 1-year period is given by P(t) = 120 +…

A: According to the given data, we have

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A: Given dataThe variable y varies directly as the fourth power of x, and when x=3, y=486

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Q: A garden shop determines the demand function q = D(x) = when the price is x dollars per plant. 4x +…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: lim [tan 3x]2x X-> 0¹

A: Since , then    Simplify:       Move the limit under the exponential:

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Q: Q1 - Calculate x(t) for below given ODE. *-*-2x = e2t x(0) = 1,x(0) = 0

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Q: Instructions: Use L'Hôpital's rule to Evaluate the Limits

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Q: 1. Find the first and second derivatives. (b) g (t) = sin(t) + 2 cos (t) 1 43 x² (c) h(x) = x² +

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Q: Solve the initial value problem. Please write your answer in teh form y = ... y² x² +1 1 dy x dx =…

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Q: Evaluate the integral √ 7x (x+4) (x²+4) -dx

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Q: A 40 inch wire is to be cut. One piece is to be bent into the shape of a square, whereas the other…

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Q: Find the distance from the point (-5,5,-6) to the line a(t) = (5, 1, −4)t + (2,−1,0).

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Q: b. Evaluate—(3x − 2)° 6

A: We need to evaluate

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Q: Convert the double integral [[ (x + y)ex²-y² dA to uv-plane where R is the rectangle enclosed by the…

A: The integral,The given lines which are representing the sides of a rectangle are,x - y = 0x - y = 2x…

Q: Solve and write interval notation for the solution set. Then graph the solution set.

A: The inequality is given as

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Q: A retail outlet for calculators sells 700 calculators per year. It costs $2 to store one calculator…

A: Retail outlets sells 700 calculator per year .

Q: 3. S dx

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A: I am going to solve the problem by using some simple calculus to get the required result of the…

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A: Formula used

Q: The vertices of quadrilateral PQRS are given below. Use the distance and/or slope formulas to…

A: Vertices of PQRS are given as below, P(-6, 4) Q(-2, 7) R(-1, 0) S(-5, -3)

Q: . Find the gradient vector field for the scalar potential function: g(x, y, z) = x arcsin yz

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Q: Evaluate the integral I sin sin³(x) cos(x) dx

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Q: W) Find the definite integral.

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Q: If m arc (WXY)= 90°, 17.1. Find the measure of the minor arc (WX). 17.2. Find the measure of the…

A: Draw a schematic diagram of given figure.Given dataA circle with center P,

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Q: Solve the given initial-value problem. (x + y)² dx + (2xy + x2 - 4) dy = 0, y(1) = 1

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Q: 2) i) Show that 5 is a primitive root modulo 17. Find the all integers, less than 17, whose orders…

A: To show that 5 is a primitive root modulo 17, we need to demonstrate that it has the property of…

Q: Part. e. True or False: f(x) x = 3, x=- 3. = x-3 2 3x-8x-3 has two vertical asymptotes:

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Q: 1. 2xy lim ; (x,y) → (0,0) x² + 2y²

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Q: √2-x x-2- x+5x Problem 1. Compute lim Show all work.

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Q: 11. Find the volume of the solid generated by rotating y = sinx, 0≤x≤, about the y-axis. Show how to…

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Q: Use substitution to determine whether the given ordered pairs are solutions of the given equation.…

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Q: 4 Find the value of the positive integral (1) (2) 1 [² (4x² - 7x + 5) e³dx (1) 5/8 S es (3) S xex dx…

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