Use the Integral Test to determine whether the series is convergent or divergent. (If the quantity diverges, enter DIVERGES.) 3 Vn +5 Vx + 5 = xp convergent divergent

Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

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Q: 5. (1 + e*/") + e*/ dy

A: Solution

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A: The given problem is solved below in detail.

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A: The objective of the question is evaluate the definite integral.

Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

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A: Let's find.

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Q: \n + 2, The following telescoping series ΣΗ 1 sin sin-1 n + 1 n + 2, n=1 TT converges to converges…

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Q: Given the area in the first quadrant bounded by x^2 = 8y, the line y - 2 = 0 and the y-axis. What is…

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Q: Differentiate y = sin¬' (sec(4x²)) A. 8x tan(4x²) sec(4x²) y' V1 - sec2 4x² В. 8x tan(4x²) sec(4x²)…

A: Given query is to find the derivative of the expression.

Q: Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

A: We have to find the angle of the largest right circular cone which can be inscribed in a sphere of…

Q: x +k a. Determine the value(s) ofk such that g'(1) = 5 if g(x) = %3D %3D x² - 2

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: the derivative of f(x) = x% (x% +x% + x%

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Q: Differentiate x + y = e2x+2y A. 1 – 2e2x+2y 1+ 2e2x+2y y' В. -1 + 2e²x+2y 1 – 2e2x+2y y' | С. ||

A: Given query is to find the derivative of the expression.

Q: Find the curvature of the curve 7 (t) = (2 cos(t), 2 sin(t), t) at the point t = 0 Give your answer…

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Q: y = 4 (2,4) A y = 2x x = 2 B y =x (0,0) Region A is bounded by the lines y= 2x, y= 4 and the y-axis.…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: dx Which of the following functions satisfy the differential equation = x? dy O x= e o y= e* O x=y O…

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Q: Determine whether the series is absolutely converger convergent or divergent. Please provide…

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Q: If f(x) = sin (a*), find f (x) Find f'(5)

A: Given function is f(x) = sinx3 we have to find the first derivative of f(x) that is f'(x).

Q: dy Suppose that x and y are related by the equation 2x - y = 1 and use implicit differentiation to…

A: The given equation 2x2-y2=1

Q: Integration of (sin(x) + cos(x)) e^x is ______________.

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Given problem:-   Find the surface area of the plane ( 15x 5z+20y=35) if it is in the first octant

Q: 3. (1 + e**) + e (1-- 0 Ans. x + ye*/y = C

A: To differentiate.

Q: Write z1 and 22 in polar form. 21 = -36, z2 = V3 +i Z1 Z2 Find the product z1z2 and the quotients 2…

A: Let's find.

Q: Solve the equation xydx - (x + 2)dy = 0

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Q: 22. Sketch the region bounded by f(x) = Vx -1 and g (x)=x-1 AND find the area.

A: Sketch

Q: Q3/ Find the limits 1. lim 2. lim Vx+2-1 X-1 х+1

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Q: 1. (sin x(cot x) = cos x OSX L.S. R.S.

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Q: Linear Programming, Transportation and Assignment Problems A. Linear Programming For items 1-4.…

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Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Solve the second derivative(y") of the following function and simplify the final results. Show your…

A: We need to find second derivative.

Q: Stan@ -1}de

A: ∫ tanθ dθ = -lncosθ+C ∫sec2θ dθ = tan θ +C.

Q: What is the solution of D.E y" – 2y' = e*sinx when solved using the method of undetermined…

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Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

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Q: Using Sandwich Theorem, the sequence 2 cos? n + 1 an = 4 - diverges converges to 0 converges to 2…

A: Use range of cos x which lies in -1 and 1

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim t-0 eSi + sin(2t). -) +…

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Q: If f(x) = 4,/¤In(x), find f'(æ). %3D Find f'(2). Submit Question

A: Given

Q: Solve the differential equation dx + xdy = x?e dy. %3D

A: Given dx+xdy=x2eydyTo find solution of differential equation:

Q: Let x'y"-7xy' + 16y= 0 be an ordinary differential equation. Knowing that y,(x)=x* is a solution of…

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Q: /2x+1 dx i fx(x* +1)' dx

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Q: Solve the equation xy^3 dx + (y + 1)e^(-x) dy = 0.

A: Given:  xy3dx+(y+1)e-xdy=0xy3dx+(y+1)e-xdy=0(y+1)e-xdy=-xy3dxDividing equation on both sides by…

Q: Find the divergence of the vector field F. F(x, y, z) = In(9x2+ 6y² )i + 54xyj + In (6y? + 5z?)«…

A: To find the divergence of given vector field

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Q: Eliminate the arbitrary constant on the given equation: y= G1r + C2e O (2? 22) y"+ (2 + 2) y- (2 2)…

A: The given equation is y=C1x2+C2e-x. We have to eliminate the arbitrary constant C1, C2.…

Q: 4ln(Arctan x) = 1- y

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Q: Evaluate the trigonometric functions at the special angles. Match the function with its value. 1.…

A: To Find : Values of the given functions.

Q: re' dy + +1 dr =0 O (y – 1) e + + In z = C 2. O-(y+1) e + Ine =C 2 O (1- y) e + 1. O 2y - e + +In=C

A: To solve given differential equation

Q: sove the fowowing, using Lagrange Multipiiers: Maximize flR, Y. 2) solaject to x2 + Ax + a4 t 2 + 2…

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