Question Consider the function f(x) below. Over what open interval(s) is the function decreasing and concave down? Give your answer in interval notation. 5x2 f(x) = 3. 50x + 1 %3D - - Enter Ø if the interval does not exist. Provide your answer below:

Q: CoS cos³ 0 5./ d0 1-sin0

A: Given problem:- ∫cos3(θ)/(1-sin(θ)) dθ

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Q: For the series below, (a) find the series' radius and interval of convergence. For what values of x…

A: Solving

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A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 5) S dy 5.)

A: The given integral,      ∫28-y2dy

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A: differential equation

Q: 2. Evaluatef dx. A. x+ C В. х C. -x + C : Antidifferentiation D.-x 3. Addition: Subtraction as A.…

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Q: (-1)" V2n2 + 5 Given: power series > (x + 1)" n=1 ii. Find the interval of convergence of the power…

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Q: 8. Find the derivative of (logsx?). dx 2 A. x In 5 1 В. x In 2 С. x In 5 D. 2x In 5

A: Solving the problem by finding the value of the derivative. For the question no 8. Option A is…

Q: Osyt . yrosx

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Q: Q3) Evaluate triple integral , dz dx dy.

A: We can calculate this as follows:

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Q: The side lengths for AABC below are a, b, and C. The height of AABC is h, Fill in the blanks using…

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Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: (b) / Vx² – 4 dx

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Q: z= x3 + xy4, x = uv4 + w3, az au az y=u- vew cuando u = 1, v= 1, w=-1 av az aw

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Q: + inf 1 п2 — Зп + 2 n=3

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Q: (-1)" Given: power series > (x + 1)" 2n2 +5 n=1 Find the interval of convergence of the power…

A: To find the radius of convergence we will find first limn→∞an+1anthen equate it to less than 1

Q: ] Using the alternating test, determine whether it converges or diverges

A: Answer and explanation is given below...

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

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Q: Determine if the improper integral converges or diverges. Find its value if it converges. Show…

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Q: If 42 | f(x)dr = 10 %3D 59 and 42 | 9(z)dr = 30 59 and 42 |. h(x)dx = 32 59 what does the following…

A: Use additive property of integral

Q: Find the sum of the following convergent series: itan-(2n – 1) – tan-(2n + 3)]. n=0

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Q: (x² + y³ )dx – –dy = 0 The equation ху Separable 1st order ODE Exact Homogeneous Linear

A: Solving

Q: an = In(n+1) – In(n) for n EN determine if the following is convergent or divergent { an } n=1

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Q: Evaluate the integral 2x 4)

A: ∫1e2x-452dx=∫1ex2-452dxSubstitute…

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Q: Determine whether the following series is convergent or divergent full solution pls and write what…

A: Let's find.

Q: 22n (2r 1)". Vn2 +1 nsider the power series n=1 1. Use alternating series test to show that the…

A: Given series ∑n=1∞  22nn2+13  (2x-1)n

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Q: Please

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Q: Consider the tollowing Maclaurin series: (-1)"x2n (2n)! COS X = for all x e R. n=0 1. Let f(x) =…

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Q: 1.5 (3-x Evaluate the integral L* dy dx using polar coordinate

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Q: Determine if the improper integral (1 e" )2 dx converges or diverges. If it converges, find its…

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Q: The task is to evaluate the function using reversed order of integration. •1 eee-x dx dy 1 Jlny

A: Change of order.

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Q: 5. In antidifferentiation, the formula f x" dx = (n+1) + Cis valid if? A. nER 6. In item number 5,…

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Q: x² +64 Using trigonometric substitution, given dx, the simplified form of the integral is: x2 […

A: Use trigonometric substitution,

Q: E. Consider two functions f and g on [0, 7] such that I f(x) dr = 9, g(x) dr = 6, (2) dr = = 4, |…

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Q: find the derivatives with use of trigonometric functions 4 y = sin 2xcos' 3x tan 2x y = 1- cot 2x 3…

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Q: 220° 12 сm 70° X =

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Q: Solve for the following integral: 1 -dx (e2x – 4)5/2

A: I=∫1(e2x-4)52  dxu=-2xdx=-12 duI=-12 ∫due-u-452v=e-u −4dv=-e-u du-dv(v+4)=duI=12∫1v52 (v+4) dv

Q: given series is convergent 2"

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Q: Given: Em 00 tanm tan m+1) q. Find the Sum of this Convergent series.

A: Given that ∑m=1∞1tan-1m-1tan-1m+1Solution…

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Q: For the functionf(x) given below, evaluate lim f(x) and lim f(x). x00 X→ー0 f(x) = -5x - 3x + 2 cos…

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