9y=x²,0 ≤ x ≤ 2 ; x-axis

Q: Given that Y₁(t) = e 2¹ and Y₂(t) = e³ make up a fundamental set of solutions to y"+5y'+6y=0, find…

A:

Q: Question Use the graph of f(x) shown below to determine each of the following limits. Provide your…

A: Find out the limits.

Q: 3 co ós co -6 -3 144 -4 Let y = ,V1= 5 -1 Compute the distance d from y to the subspace of R4…

A:

Q: News s the followinouation sutisfied Cauchy - Rieman. equation w = Z₁ W 4

A:

Q: 6. If q p² p³ - 1 9² p2 µ³ – 1 1 = 0, show that pqr = 1. - 22

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

A:

Q: Show that the following are binary operations on the specified sets. 1. Addition, subtraction, and…

A: Binary operation is the operation which is performed on two elements of a set X and the result is…

Q: (6) Using suitable transformations, evaluate closed region in the first octant bounded by the…

A: We have to solve given Questions.

Q: 1. Find when y = In (-²). dx Express your answer in a single fraction.

A: The given function,     y=lnx5-2x

Q: = X ¹0 = 1 8 = = 0 ay!!

A:

Q: ²²1559 1≤ y ≤9 Find the length of the curve_x==y 3

A: If if x is a function of y then  the length of the curve is L=∫ab1+dxdy2dy   over the inetrval a≤y≤b…

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.)…

A: The given intregration,∫sin2θ3-7sinθdθ

Q: Evaluate the following integral by using Odd and Even Powers Method: y = [₁ cos5 (1x) dx

A: We will evaluate the given integral by using odd and even power method in the following step.

Q: If ā= 3x - 5y and b = -2x+9ỹ, write the vector 5ã-85 in terms of x and y

A: Given vector are a→=3x→-5y→   and b→=-2x→+9y→. We have to find the vector 5a→-8b→. Now, 5a→=53x→-5y→…

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 7 sin(x) + 7 cos(x),…

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Q: 7. A line has equation /:*-=-= 1:*=1==32₁2=3 x-1 y-2 -,Z=3 z a) Write the parametric equation for…

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Q: In Problems 1-5, let R be the region bounded by y = x² + 3, y = 2x, x = 0, and x = 4. Each problem…

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Q: 1 6) m=1 [ n+1 7) fx.tan-2x.dx =

A: We have to solve a part 6 and 7.

Q: 5x 5 y-y-ey = e

A: Given problem:- Solve differential equation y'' -y' -2y=e5x

Q: %VIII. १:०. By using the unlimited coefficients method, choose the correct answer for this equation…

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Q: Prove that sech-¹(x) = In(¹+√¹-x²) X

A: Here we have to solve the inverse hyperbolic function.

Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector . 5. Find parametric…

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Q: Evalvate 5x-12 X (x²+4) dx

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Q: %VIII. १:०. By using the differential operator D and it's inverse, solve this equation: y"+y=sin(x)…

A: The given equation is;  y''+y'=sinx.

Q: Consider the following. f(x) = =x+4 (a) State the domain of the function. O all real numbers x O all…

A: We have to find asymptote

Q: Find (dy/dx) for: tanh ¹(x y) + e(x+y) 5 cos(y)

A: We have to determine derivative

Q: Consider the following function. Function f(x) = 8x4 - 6x³ - 165x² - 37x + 60 (a) Verify the given…

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Q: Consider the following polynomial function. f(x) = (x+2)²(x-1) Answer the questions regarding the…

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Q: The following chart shows "living wage" jobs in Rochester per 1000 working age adults over a 5 year…

A: Solution:

Q: Q5. Solve: = y² (1+x²), y(0) = 1.

A:

Q: If y = √1 − x² sin¯¹x, prove that (1− x²) ¹ + xy = 1− x². dx

A: We can prove the given the result by differentiating the given function.

Q: i/ - y - y - 6y = ex - الا و

A: Given

Q: Evaluate x³ + €

A: On solving this we will get

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t = 0

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Q: Given the initial condition y(0) = 1, find the particular solution of the equation y' = e3x - 2y

A:

Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6). Q2. Find the angle between…

A: Here are the solutions:

Q: a) Evaluate the following indefinite integral of a rational function: √9-4x² dx X

A:

Q: 4. Using the vectors: ü=[2,-1,3], v=[4,5,-2], w=[1,-1,7], calculate: a) b) ux v c) ū+ v +2w

A: Here we have to perform the vector operation

Q: T 3. Find the length of arc of the curve y = ln(secx) from x = 0 to x = 4

A:

Q: The number of bacteria in a culture is given by the function n(t) = 940e 0.1t where t is measured in…

A: To find out the relative growth rate.

Q: Find the vector standard a Ā= (-3.4.5)

A: we know that if v=<a,b,c> then its standard form is v=ai^+bj^+ck^

Q: Q6) Find the Area bounded by the curves y = √√√x and x = 2y - y² ,with sketch.

A: Let's find area between two given curves.

Q: 4x+5 x2+x-2 5) 6) 2=1 +1 7) fx.tan-1x.dx dx =

A: To evaluate the given integral.

Q: Explain why the integral is improper. 49 1 1²0 √/x dx X 1.6 1.4- 1.2

A: Given improper integral I=∫049    1x   dx

Q: Evaluate the integral: LIVE 1 I√9r²+25 dr.

A: We will solve the given question using simple Integration rules.

Q: Effect of Housing on Start Jobs The president of a major housing construction firm claims that the…

A: This question is related to rate of change, we will solve it using given information.

Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) =

A:

Q: If y = ecos(x) then y" + sin(x) y' +cos(x) = ****

A: We have, y=ecos(x) We need to evaluate, y''+sin(x) y'+y cox(x)

Q: Graph the rational function f(x)= ↑y K -12 -10 -6 -4 S -2 12- 10- 8+ 6+ 4 Y 2- -2- 4 -6- -8- -10-…

A:

Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

A: