If the series un is convergent, n=1 then the series (−1)ª un is also convergent. n=1

Q: The half-life of Radon-222 is 3.8 days. A 34-gram sample of Radon-222 is monitored for one day. How…

A: Please see the below picture for detailed solution.

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

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Q: Question Find the linear approximation L(x) of the function f(x) = cos(x) at a = - 품. (Enter an…

A: We can find the linear approximation as below.

Q: 3. Pedro walks at te speed of 40 meters/min from the school to home, by taking the longer route of…

A: Pedro walks at the speed of 40m/min from the school to home,by taking longer route of 100 m to the…

Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: Let R be the solid enclosed by the surfaces z = 3x² + y² and z = 8 – x² - y². Fill in the missing…

A: To find the missing limits of integration.

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 5, 2) is twice…

A: Let    P(x,y,z)  be the general point  A( -2, 5, 2)  and  B(6, 3, -3)PA=2PB Recall

Q: Answer true or false. The function f(t) = (et) 10 is of exponential order. O True O False

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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

Q: Find the area of the region between two curves f(x) = 3x + 1 and g(x) = x from x = 0 to x = 1.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the curl of the function G = (xcosy)i + xy² j. (y² + xsiny) k ○ (y² + xsiny) î ○ (y² - xsiny) î…

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Q: Find the particular solution of the differential equation that satisfies the initial equation= f(x)…

A: We have differential equation f"(x) = 7/x2  and initial conditions f'(1)=3 and f(1)=4

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: To find : the domain in terms of i,j and k

Q: 4 Find the arc length of the curve the interval 2≤+ ≤ 5 3 given parametrically by x= 3 + ² y = + ²,²…

A: To find out the arc length of the curve.

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: 1. A) Express 0 1 4 1+x dx as a power series.

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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: Find the G.S. about xo = 0 for th 2 (1+x²)x" + 10xy' + 20v

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Q: If u = X + y+z a) 0 y 2+x ди + then the value of x x+y x b) 1 c) u d) None ax +y + ay +2 ди əz IS:

A: Question - 21 Given, u=xy+z+yz+x+zx+y To find, x∂u∂x+y∂u∂y+z∂u∂z Formulas used:…

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: (1 + y²) dx + (x²y + y) dy = 0.

A: The differential equation is given by 1+y2dx+x2y+ydy = 0                               ........1 To…

Q: Question 9 of 20 View Policies Show Attempt History Your Answer Correct Answer Correct. Solve the…

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Q: Consider the following vector function. 1, 12², 1²) (a) Find the unit tangent and unit normal…

A: The given vector function rt=3t, 12t2, t2

Q: 3. Find the Taylor polynomial of degree 3 centered at x = 4 for the function defined by f(x)=√x.…

A: To find out the Taylor polynomial of degree 3 for the given function and also find out the value of…

Q: Determine the independent and dependent variables on the given differential equation: - (5²) -15…

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Q: If N₂- My M equation = Q, where Q is a function of y only, then the differential M + Ny' = 0 has an…

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Q: Determine whether the following series converges. 5(-1)k+1 Σ k=1 k5 Let ak 20 represent the…

A: Given: Here,            ak=5-1k+1k5 and decreasing series.  Now,…

Q: log₁ (3)

A: The given logarithm log449

Q: Estimate the area under the graph of f(x) = rectangles and right endpoints. Rn = Repeat the…

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Q: Evaluate the integral. -^x dx e S² sin √1-x² 2

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Q: 1 Σ (3)"-wn + 4 n = 0 (n + 1)(n + 2).

A:

Q: Find lim a. lim x→0* c. lim x²- - 5x + 6 2 3 x - 3x x -5x+6 b. lim x+3+ x³-3x² 2 x -5x+6 x³ - 3x² X…

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Q: Consider the following function and point. x + 4 (5,9) X-4 (a) Find the derivative of the function.…

A: The given function is fx=x+4x-4, 5,9

Q: Given the function graphed below, evaluate the definite integrals. - 4 3 یبا 3 2 1 -1 -2 3 [' = f(x)…

A: From the given graph, we have to find the value of the definite integrals.

Q: Differentiate y = (2x³ + 3x² - 1)5 30x(x + 1)(2x³ + 3x² - 1) O 5(6x² + 6x)+ 30x(x+1)(2x³ + 3x² - 1)4…

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Q: PART 2: Obtain the general solution dv V dP P Obtain the particular solution y' = 1 + y² such that…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. 4x -…

A: we use the maclaurin series of sin x to find the maclaurin series of the given function

Q: y' - y = 2 cos(6t), y(0) = 0 Find L{f(t)} for f(t) = 2 cos(6t). (Write your answer as a function of…

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Q: Find the gradient of the function f(x, y) = sin(x + 2y) O cos(x + 2y) [2î+î] cos(x + 2y) [i+1] O…

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Q: If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle…

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Q: (-9) Σ 5 0 = 1

A: The answer is given below:   Ration Test

Q: Question is to find all the local​ maxima, local​ minima, and saddle points of the function.…

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Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: (10 sin(x-sin(x-dx 6 2 (Ans: - sin(2x-2) + 5 x + C)

A: Given, ∫ 10sinx-π6sinx-π2dx

Q: 2. The table shows values of the function y = G(t). Use the table to estimate the value of 50…

A: Physical significance of integration is calculation of area under the curve. Here discrete values at…

Q: At what points is the following function continuous? f(x) = 3 x - 512 2 X-64 12, 7, x8, x-8 x=8 X =…

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Q: Let f(x) f'(x) = 3 sin r 2 + cos x Find f'(x).

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Q: How long will it take for an investment of $3,000 to double in value if the interest rate is 6.5%…

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Q: Use integration to find the area of the rose curve r = cos 20.

A: Area bounded by the polar curve Area=12∫ab r2 dθ

Q: Evaluate the line integral along the curve C. S-Tabe − ydx + xdy, C: y² = 3x from (3,3) to (0,0) O O…

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