Solve the following indefinite integrals, using substitution or integration by parts where needed 10 1+4x a) fx(4+x*)" dx b) f- V1+x+2x?

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

A: Here we have to find the volume.

Q: Solve the initial value problem using Laplace transforms. y" - y' – 6y = 2, y(0) = 0, y'(0) = 0

A: We need to solve the IVP given.

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 domain of the vector function. (Enter your answer using interval notation.) r(t) = (v 36 –…

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Q: The table gives the U.S. population to the nearest million for selected years from 1950 and…

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Q: cOs x dx sin² x+ 2 sin x+5

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Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: Consider the change of variable u = xy and v = 3y + 2x and the integral 2.r + 3y – 6 =0 - ||. (2r²y…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x2 – 16x – 4 on the interval [2, 6], how many…

A: We state Rolle's theorem here ------    Let f : [a,b] -> R be a function continuous on [a,b] and…

Q: 1 dx Vx - Vx 3

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Q: If f(x, y) = -x - y* + 3xy - 2x - 5y, then in the process of obtaining its critical points the…

A: We want to find value of b.

Q: 1) Center: (12, -3) Radius: 3) Center: (-4, 10) Radius: 8 5) Center: (-3, 9) Radius: 8

A: 1) center: 12,-3Radius: 33)center: -4,10Radius: 85)center: -3, 9Radius: 8

Q: dy y- 2x. dx = x(x+1)y %3D

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Q: 3x + 4y – 5z= - 8 4x + y- z= - 14 x- 3y + 3z = - 10

A: answer is in next step

Q: Use Stokes' Theorem to evaluate curl F· ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

A: Stoke's theorem: The surface integral of the normal component of the curl of F is equal to the line…

Q: Find all real and complex solutions to the equation   x^3 − 3x^2 − 10x + 24 =0

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Q: АСTIVITY 2 FINDING OTHER TRIG VALUES Given some initial values, apply the different trigonometric…

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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. 3 + 5 + 7 + · · · + (2n + 1) = n(n + 2) ...

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Q: Find the surface area of a sphere at the instant when the rate of increase of the volume of the…

A: Topic:- application of derivatives

Q: What is the area of the region bounded by the graphs of y = x – 2x and y = -x+2? %3D - %3D O A =…

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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: Find V· (V × F), if F(x, y, z) = 5e**i+ 5xe®j – 7ev³k. V· (V × F) =

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Q: Find the surface area of the portion of the cone z=ax +y within the cylinder x+y =1.

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Q: The function f(x) = 2+ 6x + 150x- has one local minimum and one local maximum. This function has a…

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Q: Find the equation of the tangent to the graph of f(x) = x-3 at the point (5, 4). Start by evaluating…

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Answer each question appropriately. f(x) dx = 9. Find -2 f(x) dx , if f is odd. Suppose that

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Q: D If the Taylor series expansion for f (x) is given by f(x) = Eo- (x- 2)*, then f(4) (2) = %3D

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Q: Suppose parametric equations for the line segment between (-2, 8) and (7,3) have the form: a + bt…

A: This question can be solved by substituting the values of x,y and t in the given equations.

Q: If f(x) is continuous on the interval [a, b] and a <c < b, | f(x) dæ is equal to then

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Q: Consider a wood beam (see figure) carrying a uniform load of 20.5 kN/m (which includes the weight of…

A: answer is in next step

Q: The fifth derivative of the function f(x) = 5x° is a constar False O True

A: Given query is to find statement is true or false.

Q: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round…

A: Solve the following

Q: B. Find the area of the region bounded by the following:

A: answer is in next step

Q: Solve by Gauss-Jordan elimination

A: answer is in next step

Q: Find the area of the region enclosed between the curves defined by the equations y = x² – 2x + 2 and…

A: Solve the following

Q: 2. Use the linear approximation of f(x) = x² ln(x + 1) to estimate (1.01)² ln(2.01).

A: We need to estimate value.

Q: Consider the following vector field. F(x, y, z) = xy²z²1 + x²yz²j + x?y²zk (a) Find the curl of the…

A: div F = i∂∂x+j∂∂y+k∂∂zF(x,y,z) curl F = ∇×F

Q: Given the function below f(x) = V-80x + 144 Find the equation of the tangent line to the graph of…

A: Given :

Q: Show that lim (2,v)>(0,0) **+y D0.

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Q: 22 r = 7 sin 0 + 50 cos O

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Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

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Q: find cke endefinite integral using entagrstion by parts with gle given choices of de far Oe constant…

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

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Q: Exercise 7.2 1. Calculate the values for f (x) = 3x a) f(2) %3D b) f(-2) %3D is (1; 2; 3). 3. %3D of…

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Q: 5. show that the equaution sin X-3x+1=0 has only one real root

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Q: Let ü = - 4 and i 3 , and let w = ü x v. Answer the following: Find w. Give your answer as a vector…

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Q: 6x° – 15x* + 20x – 1 and classify them using a Find the critical numbers of the function f(x) =…

A: Given the function