Evaluate using integration by parts o a) (In 3x dx

Q: Consider the following equations. f(x) = x5 + 3 g(x) = x + 3

A: Given equations f(x)=x5+3g(x)=x+3First we need to find the intersection points…

Q: Find the solution of the given initial value problem: y(4) + 2y""+y" + 8y′ − 12y = 6 sin(t) + 80e¯t;…

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Q: Find the solution of the given initial value problem. 3y""+66y'-1044y = 0; y(0) 11, y'(0) = 57,…

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Q: (v3 - 3y + 2)√√9+ x²dx + x²dy = 0

A: The given differential equation is;  (y2-3y+2)sqrt(9+x2)dx+x2dy=0. Repost the next questions.

Q: Find the radius of convergence, R, of the series. R = 00 Σ n = 2n(ln(n))² 4n I = X Find the…

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Q: 3 S4e³ lnx dx

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

Q: dx 2+2 sinx + cos x

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Q: Find the derivative of f(x) = log, (3x4 − 2x²) at the point x = 3. Enter an exact answer. Provide…

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Q: Evaluate the integral and interpret it as the area of a region. 6 •π/2 19 sin(x) - 9 cos(2x) dx

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Q: For what values of x is the function f(x)= A 2 B с The function is never increasing The function is…

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Q: Suppose the second derivative of a function f is f" (z) 0 (-∞, 1) U (1, 3) U (5,00) ○ (3,5) O (1,3)…

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√x² + y² + z² (8,…

A: Our Aim is to find the gradient of the function at the given pointwhere Function is…

Q: 4. Find the limit, if it exists or show the limit does not exist: a) b) lim 47,² (x,y)(0,0) x + y…

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Q: Determine the principal P that must be invested at rate  r = 3 1 2%,  compounded monthly, so that…

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Q: 3 dx 00 (2²+4)³/2 es or diverges.

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Q: f(x (x+1)x² dx

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Q: The function f(x) This function has a local maximum at x = with value - with value 5 + 8x + 72x and…

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Q: y' =+y(y+2), y(0) = - 1

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Q: 5x2–80 lim X-4 X-4

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Q: Find the areas of the regions enclosed by the following curves. = 2sin 20

A: To find the area of the region enclosed by the following curve.r=2 sin2θ

Q: Use a parameterization to find the flux SSF. S plane x+y+z=5a that lies above the square 0≤x≤a,…

A: We have to find the flux

Q: Find the component form of u + v given the lengths of u andy and the angles that u and v make with…

A: We can solve this as follows:

Q: f(x) = 1 |x - 51 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.)…

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Q: foo 0 dx e²x

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Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

A: A detailed solution is given below.

Q: Find an equation for the conic that satisfies the given conditions. Ellipse, foci (±3, 0), vertices…

A: Solved below

Q: Determine the general solution of the given differential equation. y"" - y" - y + y = 3et+2 NOTE:…

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Q: If P(−4, −56) is a point on ?(?) find the equation of the secant line PQ. Given Q is a point on…

A: Here we have to find the equation of secant line PQ.

Q: Write the equation of the circle centered at (2, 9) that passes through (18,7).

A: To find out the equation of the circle.

Q: valuate the iterated integral below. π/4 1 St. + S² = 0 0 y cos (x) dy dx

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Q: Je ež cos (2t)dt

A: Please see the below picture for detailed solution.

Q: Maximize f(x, y) = √11-x² - y² Constraint: x+y=2=0 )

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Q: Find the limit. lim (x,y) →→ (37,6) 5 sin y

A: We can find the answer as below

Q: (jw+4) (jw+3) (jw+2) B + (jw+3) (jw+2) A(jw+2)+B(jw+3) (jw+3) (jw+2) Ajw+2A+Bjw+3B (jw+3) (jw+2)…

A: We will use properties of partial fraction

Q: Find the solution of the given initial value problem 150y" + 25y" + y′ = 0, y(0) = −14, y′(0) = 10,…

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Q: tan x 3 sec x If f(x) ƒ'(x) = To two decimal places, ƒ' (1) = =

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Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: Consider the solid in the first octant which is bounded from above by the paraboloid from below by…

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Q: 1.) Use the arc length formula to find the length of the curve y = 3x + 2 on the interval 0 ≤ x ≤ 3.

A: Given data  y=3x+2 Interval ÷ 0≤x≤3 Formula for arc length is given by  L=∫ab1+dydx2dx

Q: Evaluate the iterated integral below. π T/4 A lago S. 0 1 y cos (x) dy dx

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: Given :fx,y=sin8x+yp0, π

Q: Solve the giv '= .3 X x³ - 2y

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Q: Evaluate d -tan − ¹ (√x + 7) = dx

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Q: Find the derivative of f(x) = 6 sin¯¹(x + 4). You do not have to expand out your answer. ƒ'(x) =

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Q: f(x)=√x+1

A: Graph of the function and equation of the function is given, we have to find its domain and range

Q: Determine whether the geometric series is convergent or divergent. 64 5 (5-8 + convergent divergent…

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Q: 2. Find the curvature of f(x)= x cos²x at x = π

A: The solution is given below

Q: Find f'(x) for f(x) = A f'(x) - B f'(x) = © f(x)= 2x+cos²x tanx 2-2sinxcosx tanx 2x+cos²x sin²x…

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Q: 1. vdv S 602-1

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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