What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

Q: The Maclaurin series of the function f(x) = 8x² sin(6x) can be written as f(x) = Σ₂² n=0 where a few…

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Q: Perform a first derivative test on the function f(x) = 2x³ + 3x² - 36x +4; [-3,5]. a. Locate the…

A: To find out the critical points, maximum and minimum and absolute maximum and minimum.

Q: عندما r = 3 cm تكون : ع. 115 V فان قيمة ب. 110 dv dr اذا كان ar3 113 j

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Q: The geometric representation of the equation is a circle in R3. Select one: O True O False -3x²-3y²…

A: Given: -3x2-3y2=-18

Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

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Q: Question 12 a) 3] Find the value(s) of y such that the vectors U₁ = and U₂ = are parallel. b) Find…

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Q: • (-1) k2k k² k=1 Use the Ratio Test to determine whether converges absolutely or diverges.

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Q: J sin²(x) cos(x) dx

A: We have to evaluate ∫sin2x cos2x dx.

Q: Differentiate tan (x¹3t) with respect to x, assuming that t is implicitly a function of x. dt (Use…

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Q: Using Linear Equation, find a general solution of: dy x x - y - 5x4 3x² + 2x = 0 dx

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Q: Solve the given differential equation by separation of variables. e-y + e-5x - y exy dy dx

A: To find the solution of D.E.

Q: 0 = ^pz(Az + x) xpxx

A: Let's solve given diffrential equation.

Q: Use the washer method to determine the volume of the solid formed when the region bounded by y = x…

A: Solution given below

Q: The integrating factor for the differential equation (xy³)dx + (x²y² + 1)dy = 0 is y O X O None of…

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Q: Suppose H(x) = (1-2x)7. Find two functions fand g such that (fog)(x) = H (x). Neither function can…

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Q: The equation of plane through (3,-1,7) and perpendicular to the vector n(4,2,-5) is 4x + 2y5z-25 =…

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Q: Find the slope of the tangent line to the parametric curve [x = 4 cos(t) y = 3 sin(t) at the point

A: A detailed solution is given below.

Q: Choose x such that the following two vectors are parallel u= and v= O -7 O None of the others 07 O…

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Q: Using Integrating Factor by Inspection, solve: (y − xy²) dx + (x + x²y²) dy = 0

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Q: 3. f- 8xdx

A: Solve the integration

Q: عندما r = 3 cm تكون : V= r3 فان قيمة اذا كان 173 ب. 110 115 C dv dr 113 j

A: We can find the answer as below.

Q: The measure of the angle between the three- dimensional vectors u = (0, -1, -3) and v = (2,3,-1) is…

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Q: 5. f 3√xdx

A: Topic = Integration

Q: Q31 Find the Laplace Transform to the following function L sin2t cos3t

A: Solution is given below:

Q: Q2 a) Find a solution to the IVP: y" - 5y' + 4y = 0, y(0) = 6 and y' (0) = 2. b) Classify each…

A: First we shall find auxilary equation and its root then find the solutions

Q: Instruction: Integrate

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Q: Three different forces act on an object. They are: F₁ = F₂ F3 Find the net force Fact on the…

A: Please refer to the image below

Q: Find f', f", f"" for f(x) = 3r7-4r5 + 11³.

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Q: Barbara knows that she will need to buy a new car in 3 years. The car will cost $15,000 by then. How…

A: By using the compund interest formula

Q: S 3 7 39+x² dx

A: We need to solve integral.

Q: Solve the given diffential by variations of parameters 1. y" + y = cos x

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Q: The value of limx→0 ex-1-x x² by using series is о о -1 O 0.5 O 1 O -0.5 O

A: Solving the following limit problem,

Q: General solution of the differential equation 1-3xy X X X 11 2y 1 2y + 이름 4yy 1 4v ① -) (c) -음

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Q: Graph one period of the function f(x) = -sin(3x)

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Q: (g) y dx = (y - xy²) dy Oseparable exact linear in x linear in y Ⓒhomogeneous Bernoulli in x…

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Q: 27. Consider the function h(x) = 2x²e-x² a) In two or three steps, write the properly simplified…

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Q: əz and as functions of u and v if: ди dv z = 4e* ln y, x = ln(u cos v), y = u sin v H.W: find dz

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Q: (a) h(x) = x^√√x² +1 (b) f(x) = (3x² - 2x+1)³(x¹ -2r²- 3)² 4 (c) g(x) = (3-4) ¹ 5x+7

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Q: Problem 2. Solve these integrals using integration by parts 2x - 3 -da, er (a) [ 27 (b) logą (r)da,…

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Q: Graph the function. -4 X for -3 <x< -1 for -1<x< 1 -x²+1 for x ≥ 1 L X O

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

Q: Q4\Use Cramer's Rule to find the values of x, y, and z from the following equations: 2x + 3y - Z = z…

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Q: 2π 1. The region R is bounded by the x-axis, x = 0, x = 3 A. Find the area of R. sin(). 2 and y =…

A: Given: Region R is bounded by x-axis, x=0,x=2π3 andy=3sinx2

Q: Find the total area of the shaded regions. (-3,36) -6 ₂ Ау 40 32- 24- 16- 8- -8- y=4x (3,36) y=x 5x…

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Q: B-Find the area of the region inside the curve r-1+cose and outside the curve -1 and graph the two…

A: Equate both equations to find limits and intersecting points of these curves

Q: J = * By using trapezoidal rule, n=2, The integral π/2 sin (x) dx 0.9482 0.9480 0.9481 0.9444…

A: To evaluate the integral J=∫0π2sin(x)dx usiing Trapezoidal Rule:

Q: iff has n derivatives at x = a. The n" degree Taylor polynomial is the nº partial sum of the Taylor…

A: Suppose f(x) has the Taylor series at x=a which is: ∑k=1∞fk(a)k!(x-a)k

Q: - If f(x, y) = cos(2x) − x² e5y + 3y², then fxy = -10x e5y True O False O

A: A detailed solution is given below.

Q: Suppose directional derivatives of the scalar function f(P), at a point P = (x, y), in the…

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Q: Find dr/dtheta for theta^(-7/9) + r^(-7/9) = -5

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Q: S HENN -dx x4-4

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