n=1 n 2n+1 2n-1 xch

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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Q: (a) Find the general solution of each of the differential equations: dy 8e2x - 4x dy dx = 12e - 10y…

A: Solved below.

Q: 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the given a and b.…

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Q: 3 2x² + 5 can be split into simpler fractions using partial fractions decomposition. Set up the very…

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Q: What is the solution of the given ODE * xy' + y = √x /2 x = {√x + ² y = {√x + = 2 y 1 x Option 1…

A: Given problem:- What is the solution of the given ODE*   xy' +y= √x

Q: Evaluate S ( + - + e²+ =) dz 3 · 3z 21² In x++²x+}x+ + C Option 1 √√(x³)x= √√√x + √2x+C I- Option 2

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Q: f. √₁²√x (x − 2x² + 1) dx -

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Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A: To find the volume of the solid of revolution formed by rotating about the x-axis the region bounded…

Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: Find the general Solution of the complement of the following differential equation y"-y" - y'- 2y =…

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Q: Andy and Donald are both running toward the soccer ball during a game. Andy's path is represented by…

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Q: Q1: A- Write the following algebraic expression in its simplest form: 5x+3x²+5x+6 X *+3 25x²-9

A: Please refer to the image below

Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2) s²-4

A: Given :L-13ss2-4

Q: Use finite difference approximation to find the values of y(0.25), y(0.5), and y (0.75) for the…

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Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

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Q: Question 2 A. B. A system of linear equations is given below. 2x + y + 2z = 1 x + 4z = 2 y = 2z = 1…

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Q: B. Find the extreme values on the given closed interva 1. f(x) = 4x - 3; [1,5] 2. f(x) = x + 8;…

A: follow next step

Q: Find the indefinite integral. (16x +13) In (2x)dx Select the method of integration that should be…

A: Integration by parts ∫udv=uv-∫vdu

Q: what substitution formula is used here ?

A: the substitution formula used here is-

Q: The position of an object moving along a line is given by the function s(t)= - 16t+80t. Find the…

A: The objective of the question is determine the average velocity in the given intervals.

Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

A: The given differential equation,    xy2y'2+yx4-1y'-x3=0

Q: If Vf = F, then F is called a potential vector field, and f is called a conservative function. True…

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Q: dx | | dt dy dt dz dt 2x + y + 2z 3.x + 6z = -4x – 3z - =

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Q: Find all solutions of the equation 2 sin² x - COS X = 1 in the interval [0, 2π) with x₁ < x2 < x3.…

A: The given equation is: 2sin2x-cosx=1 To find the solution in the interval [0,2π).

Q: 6. If If vectors (5,2,-1) × (2,-1, a) = (5,-12,-9) then determine the value of a.

A: Given: 5,2,-1×2,-1,a=5,-12,-9

Q: Find lul, Ivl, 12ul, |2v|, lu + vl, lu − vl, and _|u| - |v|. u= 5i + j, v = 2i - 4j

A: We need to calculate the magnitudes of given vector and evaluate the given expressions.

Q: sketch the graph of fox) = 2 1+x²²

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Q: Find the average value of the function on the given interval. f(x)=√x+3; [1, 22] (Type an integer or…

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Q: Among all rectangular solids defined by the inequalities 0≤x≤a, 0≤y≤b, 0≤z≤ 1, find the one for…

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Q: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: The equation P=25sin(2πt)+90P models the blood pressure, P, where tt represents time in seconds.…

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Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for fæ(t) =…

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Q: 1 If sin(0) and is in the 4th quadrant, find cos(0) - 8 cos(0) = Enter your answer as a reduced…

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Q: Find the linearization of the function f (x) 1 9x+8 at = -1. L(x) = -9x-10 si Find the true values…

A: This question can be solved using the concept of linearization of function.

Q: a 1. The graph of y = where a is a constant is called the witch of Agnessi (named after 2 x²+a² the…

A: To find the derivative and equation of line tangent to the given curve.

Q: √√1-25x² dx

A: This question can be solved by the concept of some special integrals.

Q: 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258 (c) 82 (d) 734…

A: Given problem:- 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258…

Q: Question 10 The parametrization describes a cone. O True O False r(u, v) = (u, sin v, cos v)

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Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

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Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

A: We need to s0olve D.E.

Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Given

Q: 2 sin(x − 57) + 4 5 4 3 2 1 Sketch a graph of the function f(x) = -3/2 -5/4 -I -3/4 -π/2 -π/4 -1 -2…

A: The general form: a sin (bx – c) + d Where, |a|  = Amplitude 2π/|b| = Period c/b = Phase shift d =…

Q: Q3) Assume A = [4 6 3 11 7 2 [32] and B = 1 14 5 show that (AB)' = B' A' 31

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Q: S'Xªv2x² X³² √2x² + 4 dx

A: Concept: The reduction formula: The reduction formula is regarded as an integration method.…

Q: Given the definite integral, its limits are to be substituted to x³ dx x + 1 x² x² 2 x3 3 Option 1 +…

A: Given problem:-

Q: If u and are orthogonal to each other, then u x O True False = 0.

A: Given :u→ and v→ are orthogonal

Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

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Q: 3. y= x²-3x-4 x+2

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