Solve the given dif fential by variations of parameters 2.y" + 2y + y = e Int

Q: Find all solutions of the equation in the interval [0, 2π). cos3θcosθ+sin3θsinθ = -1 Write all…

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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: Let a = (5, 4, 2) and b = (-1, -2, -3), then 3a 5b (10, 2, -9). = - Select one: O True O False

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Q: A construction worker pulls a five-meter plank up the side of a building under construction by means…

A: Solution

Q: S HENN -dx x4-4

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Q: Determine the point on the curve y = 19x² closest to the point (0, 5) with x>0. What is the slope of…

A: See this solution in below.

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: Verify that y = c₁ex + c₂e4x is a solution to the DE: y" - 5y + 4y = 0.

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: Find the critical points of the function f(x) = 4 cos² (x) contained in the interval (0, 2). Use a…

A: Follow the procedure given below.

Q: The length of the curve r = sin² for the period 0 ≤0 ≤π is 6 O 2 O 8 O 4 O O None of them

A: Use derivative and length of curve formula for polar curve.

Q: x cos 3x dx

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Q: The graph off-1 is given below. Graph the tangent line to f-1 at the point P(1, 1) for f(x) = -x³ +…

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Q: Use the Limit Comparison Test to determine if the series converges. k³ +7 k(k+ 3) (k − 2) (k+1) k=1…

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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: Problem 1. Solve these integrals using substitution (a) [ x(x r(x - 2)5dx, (b) [te²³² test dt.

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 So dx 6 x+8 Write your answer…

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Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

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Q: 2. Find the unit tangent vector for the curve r(t) = (t cost, tsin t).

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Q: Evaluate the following integral using change of coordinates: SR S x³ + xy²dady where R is the region…

A: Let's solve given double integral.

Q: SC₁+ Fuj³d₂ dn

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Q: b.) Draw the projection on a xz plane Show solution for the equation 4 اس -2 7 z 3 2 0 -2 1 2 c.)…

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Q: Find the area of the region that is bounded above by the curve f(x) = (x + 2)² and the line g(x) = 4…

A: NOTE: Refresh your page if you can't see any equations. . here we have first, we need to find the…

Q: Test the series below for convergence using the Ratio Test. n+ 3 3n+3 n=1 The limit of the ratio…

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

A: As per our guidelines, we are supposed to solve only 3 subparts. Kindly post other parts in the next…

Q: following function L sin2t cos3t

A: let  f(t)= sin2t cos3twe use the formula 2 sin  A   cos B = sin(A+B)+sin(A-B)

Q: The determinant for the following matrix is [511] L4 2 O C 10 2

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Q: 2. (x² + y² + 1)dx + x(x − 2y)dy = 0

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Q: Find the area of the surface obtained by rotating the curve about the x-axis. 2) 20 sys 3 Select the…

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Q: If √²₁ √√1-y² x² + y² dxdy is changed to equivalent integral in polar coordinates, then the…

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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 =…

A: we know that if a plane is  perpendicular to a vector then the  normal of the plane is parallel to…

Q: Evaluate the function for the given values of x. h(x)= Part 1 of 5 h(-3)= Part 2 of 5 -5x+7 for x…

A: The given function,   hx=-5x+7for x≤-23x+2for -2&lt;x&lt;34for x≥3

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

A: Given:

Q: a. (f+g) (x)  the problem is f(x)=3x+4; g(x)= 2x-3

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Q: The integrating factor for the differential equation (xy³)dx + (x²y² + 1)dy = 0 is

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Q: Find the total area of the shaded region shown to the right given by the curve y = 2( sin x)√1+…

A: We can solve this as follows:

Q: X Evaluate the integral [sincos dx. X sin cosdx= 5 C

A: The objective of the question is evaluate the indefinite integral.

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: Find the principal unit normal vector to the curve at the specified value of the parameter. (Give…

A: Please see the below picture for detailed solution.

Q: Determine the Inverse Laplace transform for 5s + 2 C-¹{² +65 +13) 1- f(t)= 5e³ sin 3t+ 13 e³ cos 3t…

A: Given problem:-

Q: \(\) The geometric representation of the equation -4x² - 4y² = -12 is not a cylinder in R². Select…

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Q: Evaluate the integral S√² - 4 + 3s ds = S√-4 - 4 + 3s ds.

A: The objective of the question is evaluate the indefinite integral.

Q: f(z) The residues of 4z (z − 1)(z + 2)² 4/9,-4/9 O 4/9.4/9 O -4/9, 4/9 O -4/9,-4/9 O 4/7,-4/7 O

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Q: Find the general solution of the given differential equation. 3 +24y = 8 dy dx y(x) = Give the…

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Q: 2" The value of p for the series En=1 by using ratio test is n! -1 O 8 2 0 ( 1 O

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Q: L[-te-at * u(−t)]:

A: Solution given below

Q: Let a be a real number. Evaluate the following integral: So f +ydady

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Q: dy (8) The solution of differential equation: + y = xy³ is dx (a) = x + ²+ce²ª, y (b) = x² + + ce²x,…

A: Using differential equations

Q: Of all rectangles with a perimeter of 28​,which one has the maximum​ area? (Give the​ dimensions.)

A: We can find the dimensions as below.

Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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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