Find the second order derivation for y = e-3x².

Q: Determine the general solution of the given differential equation. y"" - y = 11 sint NOTE: Use C₁,…

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Q: Solve the following system of equations. 3x+4y = 4 6x+4y = 16

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Q: Find the interval of convergence of the series. (5x) n².4" n=1

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Q: The rate of change of revenue (in dollars per calculator) from the sale of x calculators is R'(x) =…

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Q: -2y -2y (²²7) dx + e dy = 0 ex + x

A: Different ial eq is homogenous.

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

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Q: -10 -10 10 (c) Describe the relationship between the graphs. The graphs off and f" are reflections…

A: Let's solve for c part.

Q: Evaluate x³e¹dx O 4 0-etz ext of¥ + + C + C + C 0e**. + C

A: The given integral ∫x3ex4dx

Q: Determine whether the given set of functions is linearly independent on the interval (-∞, co). f₁(x)…

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Q: Decide which of the two given functions is linear and find its equation. 12 3 4 X 0 f(x) 9 14 g(x)…

A: Topic = Functions

Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, co).…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: Find the area bounded by the given curves. Use vertical strip x² = y - 1 and x = y - 3

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Q: errain difficulties, two sides of a fence can be built for $4 per ft, er two sides cost $8 per ft.…

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Q: Solve the differential equation by variation of parameters. y" + 3y + 2y = 2+ e* Step 1 We are given…

A: y''+2y'+2y=12+ex

Q: Find the general solution of the given higher-order differential equation. y"" - 2y" - 3y' = 0 y(x)…

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Q: 7. Determine the intersection, if any, of the planes with equations x +y-z+12=0 and 2x + 4y - 3z…

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Q: Consider the figures below. (1) 2- 14 (2) 4- O Continually increase the height of all rectangles. O…

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Q: A force of 540 newtons stretches a spring 3 meters. A mass of 45 kilograms is attached to the end of…

A: A  force 540 Newton stretches 3 meters .a mass of 45 kg  is atteched to the end of the spring and is…

Q: The given family of functions is the general solution of the differential equation on the indicated…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize…

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Q: A person starts walking from home and walks: 6 miles East 2 miles Southeast 5 miles South 4 miles…

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Q: You're studying anacondas in tropical South America, and you've decided that a particular…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

A: This question can be solved using the concept of differential equation.

Q: (-tanx) ydx + Inlexy cos x| dy = 0

A: We need to find out the general solution of the given differential equation.

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. x = eu sin v, y = eu cos…

A: To find the jacobian.

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

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Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00).…

A: Given: f1x=2+x, f2x=x, f3x=x2

Q: Given differential equation y""-ay" -4y' + 8y = e²-³x +8x⁹ (D³ - 20² - Auxilary equation 2 4D +8)y=e…

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞, ∞o). f₁(x)…

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Q: For y=x²-9x+8, find dy, given x = 1 and Ax = -0.1. dy = (Simplify your answer.) 5 2d

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Q: Tutorial Exercise Find the domain of the function. 7 |x²-161 g(x) = Step 1 The domain is the set of…

A: To solve the given domain problem of the functions.

Q: Part 2 of 8 The equation x³y-x-9y=0 is in the form of ax² + bx+c = 0. The solution set for x is…

A: Let's solve given equation.

Q: Determine whether the vector field F is conservative. F(x, y, z) = ye²i + zexj + xe k conservative…

A: We have to check if F is conservative or not.

Q: Find ||FI|. F(x, y) = i + j Sketch several representative vectors in the vector field. y O O -4 -2…

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Q: Given the unit circle, x^2 +y^2=1. Sketch the unit circle and pick a point K(a,b) on the unit circle…

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Q: Find an equation of the tangent plane to the surface g(x, y)=x²-y² at the point (7, 4, 33). O…

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Q: S D

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Q: As shown below, one of the sides has length x (in meters). Side along river (a) Find a function that…

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Q: Find all real zeros of the function. f(x) = -5x (1²-16)(x-2) If there is more than one answer,…

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Q: Find the exact length of the polar curve. r=0², 0≤0 ≤ 6π

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Q: ep 2 We have found that the roots of the auxiliary equation are m₁ = -1 and m₂ = -2. In the case…

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Q: Use the functions below to find the given value. f(x) = x - 2 g(x) = x² | = (1)(₁_ 6+ z_ d)

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Given 16y''-40y'+25y=0

Q: Find where the function f(x) = 3x4 − 4x3 − 12x2 + 5 is increasing and where it is decreasing. show…

A: Topic = Functions

Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. - 1/2 (u = v), y = 1/2 (u…

A: Jacobian ∂(x,y)/∂(u,v)= ∂x/∂u* ∂y/∂v - ∂y/∂u* ∂x/∂v

Q: xy³ lim (x,y) (0,0) x²+2y6, O a. Does Not Exist O b. Infinity О с. 0 O d. 1/3 =?

A: limx, y→0, 0xy3x2+2y6

Q: Prove the identity. cos(3x) − cos^3 x = − cos x sin^2 x − sin x sin(2x)

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Q: se e differential equation x²y" - 6xy + 10y = 0; x², x³, (0, 00). the given functions form a…

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Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A: The given surface is zex^2-y^2-1=0 and point (6,6,1).