Evaluate the improper iterated integral. x2 dy dx 1 + y2

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 3)i + tj, 0 sts1

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Q: Consider the function y-2+3x² -x³ a) Find the intervals on which this Punction is increasing or…

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: Show that the differential form in the integral below is exact. Then evaluate the integral. (-2,4, -…

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Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi+ yj – zk. %3D - V · (F × G) = %3D

A: To solve the following problem

Q: Find the derivative of the function f(x) = 4v3x² – x. 12х - 2 A. V3x2-1 6х - 2 бх — 1 C. V3x2 –1 E.…

A: To find the derivative of f(x)=43x2-x

Q: Solve following diffrential equation x(dy/dx)+6y=9x^2

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Q: _13. If y = sin(4x – 5), then what is y'? а. у'3 сos (4x -5) b. у'- 4cos (4x — 5) c. y' = -cos (4x -…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i+11 sin(t)j+4tk;…

A: Given problem:- Find the curvature and the radius of curvature at the stated point.   r(t) = 5cos…

Q: (1-) 3 4. lim

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Q: Use an appropriate form of the chain rule to find the derivative. R= e5s-t. s = 80, t= ¢!/2 %3D dR…

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Q: e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this…

A: We have to find the meaning of C'(2000).

Q: Consider the following planes. -6x + y + z = 6 18x - 3y + 6z = 36 (a) Find the angle between the two…

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Q: Evaluate sin 5x) lim, 0 (sin 5z ) 3x O 1 O 3/5 O 5/3

A: Topic:- limit calculus

Q: Find the point S so that ray (PQ) and ray (RS) are each of the same vector where P = (2, 5), Q = (1,…

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Q: complex form and COS U+ i sin o) be the polar form Idition and subtraction between two complex…

A: Topic:- complex number algebra

Q: A cylindrical container with circular base is to hold 64 in3 . Find its dimensions so that the…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Problem 37: Convert the following complex numbers from rectangular form to polar form: a. 4+ j3 b.…

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Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: Find the volume of the solid that results when the region enclosed by the geviN curves. -2X ソニ e;…

A: The given curves are; y=e-2x, y=0, x=0 and x=1. So, the bounded region is as shown below. Now apply…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 sts 1. (y – x) dx +…

A: A detailed solution is given below

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

A: Given: x=2u4-u3+u-11, y=5u3-4u2-7u+2     As we know that; The Power rule; ddxxn=nxn-1 The Quotient…

Q: Match the vector field with its graph. F(x, y) = yi -6+ 世 -5+

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Q: Find div F and curl F if F(x, y, z) = 3y°z©i – 3x*z°j – 3xy*k. div F= curl F=

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Q: Solve by Gauss-Jordan elimination

A: answer is in next step

Q: Find the exact length of the curve given by z = t° , y = t (0 <t< 4). Length

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Q: Determine the equation of the midline of the following graph. 5 3 2 -61 -37 6A 121 -1 -2 -3 -4 -5 4.…

A: see below the answer and explanation

Q: Find div F and curl F if F(x, y, z) = xz°i+ 2y'x²j+ 2z²yk. div F= curl F=

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Q: ||r(t) x r"(t)|| Use the formula k(t) to find k(t). r(t) = 8 cos(8t)i + 8 sin(8t)j + 5tk к(€)

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Q: Use Riemann Sums to calculate the area under the curve over the interval (1,3] for f(x) = x² + 2

A: By using Reimann Sums to calculate the area under the curve over the interval 1, 3 for fx=x2+2.

Q: Let 7(t) : - Find (don't include the +C) V

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Q: Area of the polar graph

A: Topic:- geometry

Q: Evaluate the iterated integral. T/4 '5 y cos(x) dy dx

A: A detailed solution is given below

Q: dx хV х2+2х-1

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Q: sheet of paper for a poster is to be 18 ft2 in area. The margins at the top and bottom are to be 9…

A: Ler the the dimensions of the sheet is  x and y in order to maximize the print area

Q: 10 dx J6 x² – 25 (a) the given integration limits (b) the limits obtained by trigonometric…

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Q: The velocity function of a moving particle on a coordinate line is v(t) = t2 + 3t − 10 for 0 ≤ t ≤…

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Q: Find the equation of the tangent line to the graph of y = -2x° + 6x? – 5x + 10 at the point (1,5) in…

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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: Determine whether the improper integral diverges or converges. 0. 8x xe dx -o. converges O diverges…

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Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

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Q: Determine whether the improper integral diverges or converges. -6x dx O converges O diverges…

A: This is a problem related to indefinite integral. Based on the general formula and concept we will…

Q: Evaluate the integral / (6x + 18y)dx + (12x – y)dy along the parabolic arc y = r from (0,0) to (1,…

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Q: Use the following information to answer the question below. lim f(x) = 3 lim f(x) = ∞ lim f(x) = -3…

A: Information of the function is given, we have to find the required values

Q: Find the standard equatron of the sphere with the given chara ct eristics center:(-1,7 9) radius: 6

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Q: Find the minimum amount of tin sheet that can be made into a closed cylinder having a volume of 108…

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Q: ||r(t) × r"(t)|| ||r(t)||* Use the formula k(t) = to find k(t). r(t), = t’i + t°j K(t) =

A: Let's find.

Q: Given f (x) = x³ + x² + x + 1 and its derivative f'(x) = 3x² + 2x + 1, find the equation of the…

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