Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and below the line y = -x . Polar inequalities for the region are

Q: Find the divergence of F(x, y, z)= x î+y³ ₂² 7 +xz³ k. O1+3y²z²+3xz O1+3y²z²+3xz² 01+3y²₂² O 1

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Q: f(x) = n=1 (7-2x)" 6n

A: The objective of the question is determine the derivative of the given power series.

Q: y' = CSC x y cotx

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Q: Bottom of the page is cut off i cannot see the solution.

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Q: Find the G.S. about xo = 0 for the following DE's 2. (1 + x²)y" + 10xy' + 20y = 0

A: answer is in next step. please give a like !!

Q: 4 3 2 14 -1 -2- -3- -4 T/2 Find lim f(x) = The graph of the function f(x) = = tan x is given above…

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Q: 1 1+exte -X dx

A: Yo evaluate the integral.

Q: The age of an ancient artifact can be determined by the amount of radioactive carbon-14 remaining in…

A: Here the age A (in years) is given by, A=-8267lnDD0 It is given that the amount D of carbon-14 that…

Q: Classify the given differential equation according to its type, order, degree, and linearity. (+)*…

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Q: For the function f(x) = 3x²-x³-4 where -3 ≤ x ≤ 3, complete the following. 1. Find f' and f". 2.…

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Q: Find the solution of the given differential equation. dx 1 y²-6y+13 dy = 0 Express your answer…

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Q: Determine whether the differential equation (7x² − 2xy + 6) dx + (7y² - x² + 7) dy = 0 is exact. If…

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Q: A botanist is studying the development of a bamboo plant. She started keeping a log of its growth 25…

A: Total time= 25 weeks Given that the plant has grown an average of 35 inch each week.  So the plant…

Q: ƒ cos(x³) x² dx. 1 ¹ cos4 + c 4 1 WIT 3 1 -| sin x³+ C 1 ·cosª + c 4 4 -3 sin x³+ C

A: Topic = Integration

Q: 1 tan 4. Express f(x) = t (Hint: Use Integration I as a power series and find its radius of…

A: Please see the below picture for detailed solution.

Q: incorrect

A: To find dy and to evaluate when x=-5 and dx=0.4 for the function y=2x4-45x+1.

Q: 8. Consider the differential equation e* (y - x) dx + (1 + e*) dy = 0. (a) Show that this is an…

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Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: Let r(t) = t²i + t cos(πt)j + sin(ät) k, find ſª r(t) dt.

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Q: The marginal cost for printing a paperback book at a small publishing company is c(p) = $0.016 per…

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Q: Consider the function f(x) = 6√x + 9 on the interval [1, 8]. Find the average or mean slope of the…

A: mean value theorem

Q: (x-2y) dx + (2x+y) dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n) and…

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Q: Find the derivative of the function g(x) g'(x) = ex + 3xe (2+3x)² = x| X et 2 + 3x

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Q: Evaluate the following limits. Show complete work x² - 4 X-2 X-2 a) lim b) lim (√x²+1-x) X→∞

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Q: Question Find the average value of f(x) Submit an exact answer using fractions and/or roots if…

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Q: 64. The complete cardioid r = 2 - 2 sin 0

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Q: Find the area of the inner loop of the limacon given by r = 1+2sin 0.

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Q: Match each of the following parametric Equations with a plane curve : x(t) = - 3t y(t) = 1 - 9t² TER…

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Q: Consider the following differential equation: y" + y = sinx - 2e and the following boundary…

A: The given differential equation is y''+y=sin x-2ex

Q: You deposited $50 into a bank that offers 2.5% interest for 30 years. A: What is simple interest…

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Q: Question Find dy and evaluate when a (Enter an exact answer.) Provide your answer below: dy = = -5…

A: The given function is; y=(2x4-4)/(5x+1), x=-5, dx=0.4

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) 200+600t 120t², where t is in…

A: The traffic flow rate across an intersection is rt=200+600t-120t2, where t is in hours and t=0 is 6…

Q: Solve the given differential equation. All solutions should be found. 2xy + y² + 1 x² + 2xy dy dx…

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Q: f cos(x³) x² dx. O 1 ¹ cos4 + c 4 1 3 sin x²+ C 1 1 ¹ cos4 + c - 4 -3 si sin x³+ C

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Q: 5. Use the definition of a Maclaurin Series to express f(2) = as a Power Series. Give the 8th degree…

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Q: 3. Explain why lim √2x - 6 does not exist.

A: 3. The given limit is limx→32x-6 Note:    Multiple questions are given, we are answer with only one…

Q: 1 0.204 as follows: Let f(x) 1 x Use linear approximation, i.e. the tangent line, to approximate the…

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Q: If the following equality is known to be true: -Ax + B x²2x-3 5 dx = -= √, ²2²3 - 2²/₁1 x - x + What…

A: Given data:- ∫-Ax+Bx2-2x-3dx=∫2x-3-5x+1dx

Q: Which of the following functions (there may be more than one) are solutions of the differential…

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Q: 3. (6x + y²) dx + 2x - 3y) dy = 0. ANS. 3x + xy² ya:

A: Here we have to solve the differential equation.

Q: Find the constants a and b such that the function is continuous on the entire real line. 7₁ ax+b,…

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Q: If u = x-y and v=x+y, then find the Jacobian matrix. о о о 312112342

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Q: (-9) Σ 5 0 = 1

A: The answer is given below:   Ration Test

Q: For each differential equation, indicate the order as a number. d'y dt4 Order is: d²y dt² Order is:…

A: Yo find the order of differential equations.

Q: dy Solve the differential equation: = A - By. Find the general solution to the dx differential…

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Q: Find the domain of the vector-valued function given below. r(t) = √√16-t²i+ 1 t+6 j+(t−4)k

A: We have to find the domain of the vector-valued function rt = 16-t2i + 1t+6j + t-4k

Q: [ (x − 7) sin(x) dx

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Q: Use Green's Theorem to evaluate the line integral along the positively oriented curve C that is the…

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Q: B) Use a known series to express ƒ(x) = e¯ as a Taylor series.

A: We need to use a known series to write the given function as a Taylor series.