Determine whether the sequence an = n° + ... + n4 + n4 n4 converges or diverges. If it converges, find the limit.

Q: (3x²+8x-12)dx In the complete factored form of the denominator is x(x+4)(x+ 3). x3+ 7x² + 12x A True…

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Q: dæ Evaluate: a/9x2 + 4

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Q: Find the area in square units bounded by the following: (Show graph and detailed solution. Box final…

A: To find the area bounded by the given curve and x axis.

Q: Determine the radius of convergence and interval of convergence for the following power series: P…

A: The given series is: ∑n=1∞(-1)n(x+8)n7n+1 Let an=(-1)n(x+8)n7n+1, n≥1

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin4x, 1+ cos4x &- 2 (А) (B) cos?2x…

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Q: 25.In solving r In(In x) dx , which substitution should be used? O A. u = In(In æ) In a O B. U = Oc.…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the alternating series (-1)"bn with n=0 1 bn 9+ 5n2

A: answer is in next step

Q: Let be the antiderivative of X). Determine the value of C if X = 12 and y= 26. (use radian form of…

A: See the details solution in below

Q: Suppose that f is a twice differentiable function and that its second partial derivatives are…

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Q: Which of the following is true? 10 @ Jsin*(x)cos°(x)dx = - cos (x) , cosº(x) cos(x) + C 4 10 (B) All…

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Q: 2х + 3, х 1 21 B 19 C 28 D) 16 A.

A: We find out the value of given integral. Follow 2nd step.

Q: 14.What is the equation of the curve that passes through (1,3) , if its slope is given by 3x? at any…

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Q: Convert the point (-7 3, 7 V3) from Cartesian coordinates to polar coordinates for 0 <0 < 2m. Give…

A: The given point -73, 73

Q: 4. (entroid š pon! of intersetion of 3 mudiens of A hriangl. FAE Ba =/3 DE AG =43 AD (ent roid ond…

A: A triangle ABC, with median AD, BE &amp; CF concurrent at centroid G. Also, AG = 23ADBG = 23BECG =…

Q: Suppose that z + y = 82. dy (1) Use the method of implicit differentiation to find dr dy da (2) Find…

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Q: Let f(x,y) = C be the antiderivative of F(x) = x-cos(2x), Determine the value of C if x = 88 and y=…

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Q: 2-/2x+1 Let F(x,y) = C be the antiderivative of f(x) =- What is the value of C if x=12 and y=9 ?…

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Q: Which of the following is true? A) All for the above ® Ssin°(x\cos*(x)dx = cos (x), cos°(x) cos1(x)…

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Q: Evaluate: Je*cos(7e")cos(4e*)dx. 1 1 + 22 1 22 sin(3e") - sin(11e") + C 22 © -cos(3e*) – -cos(11e*)…

A: See the answer below

Q: (4x²+ 5x*)dx (x+1) (x²– 6x + 34) 2 By method of partial fraction, the integral can be evaluated when…

A: Please see the below picture for detailed solution.

Q: 'x/2 dx Using an appropriate algebraic substitution, the integral - 1+x3/2 reduces to 2y² dy A 1+y³…

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Q: sech (Insinx) cotxdx=2tan-(sinx) +C A True В False

A:

Q: xcos-(x) If x =0.34 and y = 0.12, then value of C in the antiderivative of F(x)= is (use radian form…

A: If x=0.34 and y=0.12 then find the value of C in the derivative of function F(x)

Q: locate the bifurcation values of α for the one-parameter family and describe the bifurcation that…

A: To locate the bifurcation values.

Q: ind the local extrema of the function f(x,y)=e* (x² – 2y²) x-y

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Q: Using the miscellaneous substitution 2=tan match the integral expression on the left to its…

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Q: The integral expression J xsin?(2x)dx Suav=uv-Jvau u can be evaluated using integration by parts of…

A: We have to find integration

Q: sin?u In tanmudu, where m is any positive integer, we use the transformation for tan?u= cos?u (A)…

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Q: S. | sech (Insinx) cotxdx=2tan - (sinx) + C

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Q: Let x = 1.3 and y = 3.22. Determine the value of C when you evaluate cot *(2x)dx. (use radian form…

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Q: To evaluate sin 2x cos 2xdx conveniently, the formula/identity to be used islare A None 1- cos4x and…

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Q: Using rectangles each of whose height is given by the value of the function at the midpoint of the…

A: We have to find the area by midpoint and for triangles

Q: e4X dx Which of the following trigonometric substitutions is the most appropriate to the intgral…

A: Integration

Q: S x(x² – 1)dx

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Q: Using differential method, find the cube root of 600 in 5 decimal places and fourth root of 5000 in…

A: Here we have to find cube root of 600 and fourth root of 5000.

Q: Determine the interval of convergence of the following power series: * (z- 2)" Vön n= Answer: Click…

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Q: ′−6x=1 Determine the general solution to the differential equation above. (Do not include the "+C"…

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Q: Is y=e−3x+x−3 a solution to the initial value problem shown below? y′−3x=−8−3y y(0)=−3 yes or no?

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Q: xi (9a“ –10) The antiderivative of f (x) = is F (x) = 30 where "a" is equal to

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Q: Suppose a population of insects increases according to the law of exponential growth. There were 130…

A: Since the population increases by law of exponential growth.

Q: 3. Solve the initial value problem. Determine the interval in which the unique solution of the…

A: First we divide the given differential equation both sides by x2 and then campare it with y'+Py=Q…

Q: 1 Which of the following is the antiderivative of f (x) = (x+ 2). ? - Vx + 2 = « (1n (\ &a+ 2+1) +…

A: To find the antiderivative.

Q: What is the general solution for following differential equation? y′+2=−2x (Do not include the "+C"…

A: Follow the procedure given below.

Q: The integral expression Jxsin2(2x)dx can be evaluated using integration by parts of the form :UV-…

A:

Q: The given DE: (2y3-x3) dx+ 3xy²dy3D0 can be solved by: A 3 methods B 2 methods 1 method D 4 methods

A: Let's find.

Q: The equation (tan?x+3y?) sec?xdx+(3tan?x+y²)dy=D0 can be solved by A Bernoulli's Equation DE with…

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Q: Evaluate: Je*cos(7e*)cos(4e*)dx.

A: We need to integrate∫excos7excos4exdxSubstitute ex=tDifferentiate x w.r.t texdx=dtThen∫cos7tcos4tdt

Q: Which of the following is true? cos(x) + cos(7x) A Scos(3x)cos(4x)dx = J 2 J sin(4x)cos(3x)dx = […

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Q: The x2-4 dx can only be evaluated using trigonometric substitution technique. A True False

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Q: (x+1) dx If A B C + + dx ,the values of A & C respectively are (x+2) (x- 1)2 (x – 1)2 x+2 X- 1 3

A: We will evaluate the integral using partial fraction as following.