Without evaluating the constants, the partial fraction decomposition for 5x? – 3 f(x) %3D (x3 - 4x)(x² + 3x + 2)(x² + 1)

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A: We have to find convergency

Q: The particular solution y, of the differential equation y" + 4y' + 4y = 3x? + 1 is (1/8) (1-2x+6x^2)…

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Q: 4. State and prove the law of sines in triangles. 5. Prove lim,0 V2r + %3D 6. Figure out the…

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Q: The cylindrical coordinates of the point with rectangular coordinates (-V2, -v2, v2) are (v2, , V2).…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Here, the given vectors are: P(0,0,0) & Q(4,5,4)

Q: Solve the second derivative(y") of the following function and simplify the final results. Show your…

A: We need to find second derivative.

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Q: dx J1- ² 2x + x°

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Q: Question 2 ( x? Consider the function f(x) = . x2 -1 (a) Find the intercepts of the graph of f (if…

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Q: is equal to sec (2x) + In|sec(2x)|+ C sec (2x) – In|sec(2x)| + C the above the above Gsec (2x) –…

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Q: P6: x2 dx 2 – 1

A: We have to solve given integration

Q: Find the derivative of f(x)= x% (x% + x% +x%

A: Find the derivative

Q: I can't see the full solution.

A: Apologies for the inconvenience. If you do not see the Math expressions properly, then please…

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A: We need to find equation of tangent line.

Q: Evaluate the definite integral 9 6x² + 6 dx 35 X o 588.65298705274 3

A: We know, ∫xndx=xn+1n+1+C, C is a constant for any real number n.

Q: Using appropriate substitution, [sec (2x) + 1] tan(2x) dx is equal to

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Q: Solve the differential equation dx + xdy = x?e dy. %3D

A: Given dx+xdy=x2eydyTo find solution of differential equation:

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A: Topic:- derivatives

Q: \n + 2, The following telescoping series ΣΗ 1 sin sin-1 n + 1 n + 2, n=1 TT converges to converges…

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Q: Using appropriate substitution, [sec (2x) – 1] tan(2x) dx is equal to

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Q: Find the differential equation of a family of circles, each having its center on the line y x and…

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Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Given: a= 22, c=24.1, zB = 67 C A Solve the triangle. (Do not round until the final answer. Round…

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Q: I need the graph of the solution and describe its behavior as t increases

A: Apologies for the inconvenience. The solution is: yt=-1+5t3e-13t [used t place of x in the original…

Q: 6. sech(4x) tan (4x) dx

A: We need to evaluate integral.

Q: Ssec10dE

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Q: Find the general solution of the given ODE * (y² – y) dx + x dy = 0. - y=c 5 +4x + k Option 1 Option…

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Q: 5 Find the eigenvalues of the matrix A = 2 -8 -8 = Enter both values separated by a comma.

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Q: Convert the Cartesian equation x² + y² -2x= 0 to a polar equation. x2 + y2 -2x 0= O 2=-2 cos e Or= 2…

A: Given artesian equation,x2+y2-2x=0Put…

Q: dy 3) y = u5 and u = 3x – 1; 2 Ans: 2 = 15(3x – 1)* %3D dx dx

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Q: The technique used to prove that dk =- 3x + 3V3 tan" + C %3D x2 + 3 3 is O Integration by Parts O…

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Q: 3. T The point 2, 3 is given in spherical 4 coordinates. Its rectangular coordinates are: 3 /6 2 2 2…

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Q: Find the general solution of the given ODE * dy 3z+2y dr 3= -23x+2y +c 2=-23x+2y +C O Option 1…

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Q: Answer what is required in the problem. d 1 -dt 1+t dx .17

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Q: In Exercises 5 through 18, sketch the given region R and then find its area. 5. R is the region…

A: The region bounded by the lines y=x, y=-x and x=1

Q: solve the following first order differential equations (Homogeneous Equations)

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Q: For the differential equation (x -4)y" + (x- 2)y'+ 2y 0, the singular points are: O None of them x-3…

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Q: At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

A: We have to find the point where the angle is greatest

Q: x-1 y = log. x+1

A: Topic:- application of derivatives

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: (y In a In y) da + dy = 0 O In In y + T Ina += C O y= eCa 1 y%3D O Iny Ce

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Q: Differentiate x + y = e2x+2y A. 1 – 2e2x+2y 1+ 2e2x+2y y' В. -1 + 2e²x+2y 1 – 2e2x+2y y' | С. ||

A: Given query is to find the derivative of the expression.

Q: dy Differentiate implicitly to find dx e**y = 8x + 3y +8 Evaluate the derivative of the each side of…

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Q: Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) X-1…

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Q: For the differential equation (x² – 4)y" + (x – 2)y' + 2y = 0, a regular singular point is: X=4 x=2…

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Q: x-1 y = log, x+1

A: We know, ddxlog(x)=1x ddxu(x)v(x)=v(x)u'(x)-u(x)v'(x)v(x)2 log(ab)=log(a)-log(b) log(a)n=n*log(a)

Q: 1 is convergent or 1) Use the Integral Test to determine whether the series divergent. ' (3n– 1)?…

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Q: 8. (y- 2x)dx - x(1- xy)dy 0 Ans.

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