Solve the initial value problem O y = 7cost + sint O y = e-cost + 7e-¹ sint ○ y = e¹¹ +7e="t ○ y = 7e¹¹ + e-71 O y = 7e-cost + e-7 sint O y = cost + 7sint y" + 14y + 50y = 0, y(0) = 1, y'(0) = 0

Q: The point (a, b, -7) lies on the line L1: [x,y,z]=[3,−1,4]+s[4,3,−1] Determine the values of a and…

A: Given: To determine: value of a and b

Q: R is the region bounded above by the function f(x) = −2x+1 and below by the function g(x) = 2x/3 − 8…

A: Area bounded by two functions f(x) and g(x) over the interval [a, b] can be determined as…

Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

A: Given that, A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another…

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: 1 r+5√√x+6 dr

A:

Q: • (√x + 1)² √√x -dx

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Q: 7. Given A(3,1,0), B(1,0,2) and C(5,2,−2) determine the following: a. AB b. AC- c. Are points A, B,…

A: The objective of the question is determine the distance and check the collinearity of points.

Q: In Exercises 101-108, assume that each sequence converges and find its limit. 101. a₁ = 2, an+1 102.…

A: The objective of the question is determine the limit of the given sequence.

Q: If u = 4j - 2k and v = 27 − j + 7k, find ū. v. Select one: √110 O -18 O √18 O 18

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Q: 2. Letf: R→R be defined by f(x) = 4x -x2. Let B be the range of f. (a) Find B. (b) Fins f-1([0, ∞…

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Q: Q2.B. A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is…

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Q: Solve the initial value problem y" + 10y' + 25y = 0, y(-1) = 6, y'(-1) = 6. y(t) =

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Q: 4. Solve the following DE using a suitable type of transformation. y' = x + y (let v = x + y) O y =…

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Q: Draw the function y = √x-8

A: The 5 points are the following.

Q: Find dy/dx if y=3x2 – 2x.

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Q: B: solve the system of equations by Grammer Metho 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 x₁ + 2x₂ +…

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Q: 2. Find the square roots of the complex number: Z = 3+4√7 i

A: We have to find roots of given complex no.

Q: \(\) The vectors u= and U= are not orthogonal if and only if x=-136 Select one: O True O False

A:

Q: Perform the following steps to find the maximum area of the rectangle shown in the figure. C: 3 A(x)…

A: As per our guidelines we are supposed to answer only ? 3 sub- parts ( if there are multiple sub-…

Q: 65. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3-x²…

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Q: Find the points on the surface z²2=xy+1 that are closest to the origin using LaGrange multipliers

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Q: 1. Find the solution of the following differential equation? Then find the particular solution with…

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Q: at what value(s) of x does the graph of g(x) have relative minimum(s)? justify your reasoning

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Q: 21. If g(x) = A. =/20 C. 2 {22² (x² + 2, x ≤ 1. (2x + 1, x > 1' then g'(1) is B. 1 D. 3

A:

Q: 1. Evaluate the iterated integrals. In 3 In 2 (a) f f e** dydx S S 00 (b) ff X 00 (xy+1) dydx (c)…

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

Q: 58. A. Which of the following differential equations has x² – 4y² = 8 as a solution? no gai dy dx =…

A: Derivate the given equation with respect to x.

Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

A:

Q: on what intervak of x is the graoh is g(x) increasing? justify your reasoning

A: To determine the interval of x for which the graph of gx is increasing.

Q: Q3) Find the average value of the function f(x)=√cos 4x+1, on [0,1 Q4) Using Numerical Integration…

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Q: Question 10 of 17 > dh\ dt =2 5 The variable h is the height of the ladder's top at time t, and x is…

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Q: The acceleration function (in m/s) and the initial velocity are given for a particle moving along a…

A: The given acceleration function:at=t+4.Also, if v is velocity function, then v0=6.The given interval…

Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

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Q: Simplify the algebraic expression. x² + 2xy+y2 y x X x y x²+2xy+y² X x y y x

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Q: \(\) The point (5, -1, -7) is not the center of the sphere represented by the equation x² + 10x + y²…

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Q: Evaluate the following indefinite integral by using the given substitution to reduce the integral to…

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Q: 63. 100% los telborey adi The graph of g consists of a semicircle and two line segments for -4 ≤ x ≤…

A: To find the area between the given curves.

Q: Finding nth Partial Sums In Exercises 1-6, find a formula for the nth partial sum of each series and…

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Q: [(x+1)e(x²+2x dx

A: The given integral,         ∫x+1ex2+2xdx

Q: 66. Write the definite integral that computes the volume of the solid generated by revolving the…

A:

Q: The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a…

A: To find velocity at time t  and distance travelled during given time interval.

Q: Evaluate the following antiderivatives. f (x sinh x + 1) dx

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Q: Given f(x) below, find f'(x). Do not include "f'(x) =" in your answer. f(x) = (3x³ + 3x² - 4).x²

A: Given, f(x)=(3x3+3x2-4)x2

Q: f(x) = 6x3 - 9x + 4 +4

A:

Q: Find the solution of the initial value problem y" + 16y = 0, y(72) = 8, y¹ (72) = -16. Sketch the…

A: Given: y''+16y=0

Q: Find a result by using undetermined coefficients for ý - 5ý +6v = xả + e2x + 3 sin2x

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Q: For the function f(x) = 7x³ - 2x² + 2x +9, find f''(x). Then find f''(0) and f''(9). f'(x) = Select…

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Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

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Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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Q: write this on paper. I need a step by step handwritten work not just the online calculator

A: Given the series,     ∑k=1∞3k3+3k2+5

Q: For the initial-value problem: y = 1+2, 1st≤ 2, y(1) = 2, h = 0.25, the mesh points (t) can be…

A: I am going to solve the given problem by using some simple calculus to get the required result.