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

Q: If then, find f'(x). O f(x) = ²* √e² + 1 dt, 2√e +1 O None of them. O Ve +1+ C O √e™ +1 e

A: Use fundamental theorem of calculus for finding the derivative

Q: If w = f(r,s,t), r = x-y, s = y - z, t = z − x then aw дw ?x + О O -1 -2 Əw дz 1 2 (

A: It is given that, w=fr,s,t, r=x-y,s=y-z,t=z-x.   The objective is to find the value of…

Q: CONVERSATION/OBSERVATION Understanding Types Of Graphs 1. Imagine you were given three different…

A: According to the company rule, we can answer only first question and rest can be reposted.

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: find the general solution (x - 2y + 3) dx + (x-3) dy=0

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Q: dx dt Please give an exact answer. If z² = x³ + y², = dt 1, dy dt Provide your answer below: = -1,…

A: The objective of the question is evaluate the derivative of the given function at given point.

Q: Please recheck it, the answer is wrong. It isn't 823.

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Q: The symmetric equation of the line that passes by P(1, -1, 1) and Q(3, 2, -1) is: Select one: ㅇ블 x+1…

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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: Given d = and v= -5d +30=< find-5d +3v..

A: The calculation follows easy.

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: Consider the region B under the graph of y = 5x² + 3, x [3,5], and above the x- axis. Estimate the…

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Q: ·S In (x) √xln(x)-x =dx

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Q: S In (x) √xln(x)-x =dx

A: Please see the below picture for detailed solution.

Q: The graph of y = f(x) is shown. Use the graph to answer the question. 2 1 f(x) 1 -1 -2 2 lim Find…

A: Given graph of function y = f(x)

Q: The Maclaurin series of the function f(x) = 8x² sin(8x) can be written as f(x) = Σ" 72=0 where a few…

A: Solution is given below:

Q: (a)[1 Show that the following equation represents a sphere, and find its center and radius. x² + y²…

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Q: 3. What is the distance from the line to the plane? 7-(2,3,8)+(1.1.1) 2x - 5y + 32 + 1 = 0

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Q: Calculate the definite integrals (a) I₁ =¹7 (2x − 1)(x + 2) dx - 18 (b) I₂ =2₂¹8 (x + 2)(√√x - 2) dx

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Q: Let f:R-R,g: RR and h: R→→R be differentiable function such that f(x)=x²+3x²+4 g(x)=x and…

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Q: J sin²(x) cos(x) dx

A: We have to evaluate ∫sin2x cos2x dx.

Q: The equations of three lines are given below. Line 1: 6x+4y=-8 Line 2: y = x-3 Line 3: 3y = 2x+4 For…

A: The given lines are:Line 1: 6x+4y=-8Line 2: y=23x-3Line 3: 3y=2x+4

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

A: Given: Lsin2tcos3t

Q: If a = (-1, 1, 2) and b = (1,3,1), then which of the following gives |ab|? Select one: O √9 O -√9 O…

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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: Let a be a real number. Evaluate the following integral: So fx + y dxdy

A: We have to evaluate the integral ∫0a∫y-1y+1 x+y dx dy  where a is a real number.

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

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Q: If a xi = 0 and a x j = 0, then Select one: O a is equal to i + j a cannot be determined O a is…

A: Find out the correct option.

Q: Given the conic section = Intercept(s): Focus (foci): 1 5+7 sin(0)' find the x and y intercept(s)…

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Q: (9) The differential equation M(x, y)dx + (2ye* + y²e³x) dy = = is exact if (a) M(x, y) = e2x y² +…

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Q: Let a = ( − 4, 4, − 3) and b = (0, 2, 1). Find the angle between the vector (in radians)

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Q: Match the given differential equation with one or more of the solutions. (Select all that apply.)…

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Q: I sin²(x) cos(x) dx

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Q: fx tan x x dx

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Q: Let à = (1, − 1, — 5) and 6 = ( – 5,0,− 1). Find the projection of b onto a. proj¡ b = >

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Q: (b) Use the Fundamental Theorem of Calculus to evaluate the integral .8 So da dx x-6 x+8

A: Need to use the fundamental theorem of calculus to solve this integral.

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

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Q: Given the series: 1 1+ + + 9 27 does this series converge or diverge? diverges converges 00 If the…

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Q: The evaluation of 2xe³ dxdy is 3e-1 O e-3 e-1 O None of them O -3e

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

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Q: lim f(x) x → -2+ lim f(x) x →-2- O False O True 4 3 2+ 1+ -5 -4 -3 -2 -1/ 1 2 3 4 → 5x

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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: 1. Use a trig substitution to evaluate √9-x² 3√3/2 x² -dx.

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Q: :.S •√ √x(x² – 3x + 2)dx

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Q: ains 200 liters of fluid in which 30 grams of salt is dissolved. Pure water is then pumped into the…

A: Please refer to the image below

Q: Evaluate the following integral: 2² ²₂ 2² x+yz dædydz

A: Solution given below

Q: Find dy/dx if xy+2x+3y=1

A: Find dy/dx  if xy+2x+3y=1

Q: Evaluate the following integral: SS², 2*x+yz dadydz

A: Solution given below

Q: The solution of Yh = e²x (c₁ cos x + C₂ sin x) homogeneous part (yh) of the equation y" - 2y' + 5y =…

A: Let's solve.

Q: 25. f(x): Determine the value of k so that f(x) is continuous. Show work. 2x² - k x < 2 = 2x² - 5x -…

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