Date: Afincduse Partial fractin -2X+4 2.

Q: y" +y' – 2y = 4e* – 2x

A: We have the given differential equation is y''+y'-2y=4e-x-2x2     …..(1) The auxiliary equation for…

Q: Reorder the equation y=x^2-4x+3 into the form y=(x-h)^2+k

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Q: sec® x dx cot x SE V

A: We can evaluate the given integral by using the substitution u= tan x and the following formulas.…

Q: Solve x³x²-x+2=0 by Cardano's method.

A: As per the question, we are asked to solve a cubic equation, specifically x3 - x2 - x + 2 = 0 using…

Q: Problem 1. (Line Integration) Consider the curve c(t) = (e*, e-t) with 0 <t<1 and the vector field…

A: Given:

Q: NIFN dx √2x (√2x + 9)

A: Given query is to find the value of the integral.

Q: How to find the lactus rectum if (x-4)^2 =-16(y+1)

A: Length of the latus rectum is 4a

Q: Ely)-[i -2x -e-3x -3 15e-Qx -Le-3x 9 ㅇ @ CyJ= 15e-ax-e-3x dx 9 -3 € cy)= [15e -e-3x -3 15e-2x + -1…

A: e-2xe-3xx=e-2x-3x=e-5x

Q: (e2x-1)² dx e 2x

A:

Q: Calculate facterial funchion n -X x e %3D

A: Using integration by parts solve the integral:  ∫0∞xne-xdx=∫xne-xdx0∞…

Q: 5. a) Find the volume of the solid bounded by the paraboloid z= 2(x? + y²) +3 and the cylinder x? +…

A: (a)  Find the volume of the solid bounded by the paraboloid z=2x2+y2+3 and the cylinder x2+y2=1 and…

Q: 4x^2 - 10x + 4y^2 + 9y - 5 = 0 Find (h,k) and the radius.

A: 4x^2 - 10x + 4y^2 + 9y - 5 = 0 Find (h,k) and the radius.

Q: t seel dx

A:

Q: Use graphical methods to find two solutions to thesystem

A: Graphical method: The point at which graphof two equations intersect is the solution of both the…

Q: ifferentiate the funtion y = 2 csc (1-3x)

A: Giveny=2cosec(1-3x)Aim: dydx

Q: exapy %3D 4-x2

A:

Q: In 1-21, use the definition of an improper integral to evaluate the given integral. 5 2. S dx…

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Q: 29. P(x) = x°(x + 2)(x – 3)²

A: 29. Given polynomial function, Px=x3x+2x-32 To sketch the graph of this polynomial function.