27. Find vertical asymtote(s), if any, of the following rational functions: f(x) = (b) x = 2, x = ±i (c) x = 2; x = -; 6x2+x+12 (Зт2 - 5х-2) (12+1) (a)x = 2; x = - ; x =± i 3; x = +i %3D (d) x = (e) y = 2; y = %3D %3D 3

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Q: Find f(x) by solving the initial-value problem. f '(x) = 6ex − 10x; f(0) = 15

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Q: b. Find x from the following equation. log 42x = log,27*-1 7x-3 c. Express x+2x2-3x in the form of…

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Q: Find the decomposition of the given rational function into partial fractions over R. (9s)/(s^2+…

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Q: 2. Express the general solution in terms of Bessel functions: 4x²y" – 4xy/ + (16x² + 3)y = 0

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Q: Construct a general solution involving two arbitrary functions to the PDE 20 0Pu(x, 1) _ ô²u(x, 1) _…

A: Comparing it with Auxx+Butx+Cutt form, we get A=20, B=-1, C=-1. Then, B2-4AC=(-1)2-4(20)(-1)=1+80=81…

Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

Q: Q4. Evaluate "by partial fraction' x³ + 3x2 + x +9 -dx (x* + 1)(x² + 3)

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Q: Question 7 Consider S= Sx- x-m+ A) 5 3x5 3x4+6r³-3x²-6x A B C -+ -+- x-1 x+1 x+m 17/6 14/3 -dx.…

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Q: Express the rational functions as partial fractions: x² + 1 (divide first) x + !

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Q: -4x+1 dx (x+4)(x² +1) (b) Evaluate by partial fractions: (c) Find th

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Q: 14 (1). If f (x, y) = -x³ + y* - 3xy + 9x? + y, then in the process of obtaining its critical points…

A: Given that fx,y=−x3+y4−3xy+9x2+y

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A: We need to find solution in Bessel function.

Q: 1 Given the function x2 (x+1) Write in Partial Fractions 1 Hence find f: dx x2 (x+1)

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Q: 2 about the The second degree Taylor approximation for the function f(x) = point c = 0 can be used…

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Q: Consider the rational function 2x5 f(x) = 9x4 + 4x3 – 18x² – 28x + 12 2x3 x2 + 6x – 3 where 2x – x²…

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Q: Express the rational functions as partial fractions: 1 (x - 1)(x² + 1)

A: We need to express the rational functions as partial fractions.            1x-1x2+1

Q: 5. The function h(x) = x² + bx² + d has a critical point at (4, -20). Determine the constants b and…

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Q: 12 By using partial fractions, show t 1 x² -1 2(x+1) 2(x–1)' Hence, evaluate dx

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Q: 1. Evaluate each of the following integrals: X - 3 - dx x' - 6x + 8 a) 6. 1 -dx x² - 6x + 8 b) use…

A: a) To evaluate ∫x-3x2-6x+8dx Factor the denominator polynomial: x2-6x+8=…

Q: Find f(x) by solving the initial-value problem. f '(x) = 8ex − 4x; f(0) = 12

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Q: 5) Find the general solution by using reduction of order method to t'y" – ty' – 3y = 0 given that y,…

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Q: Consider the following initial-value problem. f '(x) = 9x2 − 8x, f(3) = 47 Integrate the function  f…

A: NOTE: Refresh your page if you can't see any equations. . take integration  .............(1)

Q: S de x² –2 x+1 A x2 --x - In Ix + 11 + C C x2 +x - In Lx + 11 + C B x² -x + In Lx + 11 + C x2 +x +…

A: Given ∫x2-2x+1dx. The objective is to evaluate the integral.

Q: Use the method of variation of parameters to solve the initial value problem x'=Ax+ f(t), x(a) = x₂…

A: We have to find the solution x(t) using the method of variation of parameters.

Q: 14 (1). If f (x, y) =-x' + y* - 3xy + 9x? + y, then in the process of obtaining its critical points…

A: The given function is fx,y=-x3+y4-3xy+9x2+y partial derivatives are fx and fywith respect to x and y…

Q: Show that for any ly ≤ 1 and|x| < 1. 1- xy 1-2xy + x² = Σ Tn (y)x" n=0

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Q: Find f(x) by solving the initial-value problem. f'(x) = 3e*- 10x; f(0) = 5 %3D f(x) %3D

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Q: 1 1. S dx х2-5х+6

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Q: For a. y′ =ln(y)+x,withy(1)=1. (Here x0 =1.) b. y′ =ln(1+y),withy(1)=0. (Here x0 =1.) Is it…

A: Solving for  a) y'=ln(y)+x            dydx=ln(y)+xdy=ln(y) dx+x dx Integrating:           ∫dy=∫ln(y)…

Q: 2. Integrate the rational function below without using partial fraction decomposition. S -dv

A: Integrate the rational function below without using partial fraction decomposition v2/(v6-1)

Q: 17 Use partial fractions to find dx x+ 2 xp- d* a. b. x(x +2)(x-1) x dx (x-2) a dx с.

A: As per our guide lines we need to solve only two questions please repost the other questions as a…

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Q: If f(x, y) = -x - y* + 3xy - 2x - 5y, then in the process of obtaining its critical points the…

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A: Let's solve  given integral.

Q: 7] The Wronskian of the functions 1, x, and e -2x is (а) е' -2x (2x+1) (b) 4e-2x (c) -e(2x +1) (d)…

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Q: 2t³ +11t+8 3 t³+4t² +4t 7. S -dt

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Q: 30. It is given that the graph of y=-x+mx-n touches the x-axis at one point. Suggest two pairs of…

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Q: 3 Find absolute extrema for fCx) = x°-9x´+15x -3 %3D in terval [o,3] Oへ

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Q: Where does x3 f(x)= х2 —1 have a critical point, which is not an extremum? O At x=-V3 O At x=-1 O At…

A: Second derivative test :  when a function slope is zero at 'x' , then the second derivative at 'x'…

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Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.