(2) S 1 x= V1-x²

Q: 1– 2s F(s) = s² + 4s + 5

A:

Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: 12. f(x, y) = x' – 2x – y + 4y, P = (1, 2). -

A:

Q: 7 (a) F(s) %3D (s+3)³ 2s – 3 ( (b) F(s) = s2 + 2s + 10

A:

Q: 4 (iv) F(s) = s2 +9 2s + 16 (v) F(s) : s2 + 4s + 20 3s – 15 (vi) F(s) %3D 2s2 – 4s + 10

A: The Laplace transform of a function is an integral that converts the real variable into complex…

Q: 3+2s 17. F(s) %3D (s+4)(s²–3)

A:

Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: 13. f(x) = {1 + x, 1, -5 <x <0 0 sx <5

A: Fourier series

Q: determine L−1[F].

A:

Q: 1-Vy dy Vy 4

A: We need to find the given integral.

Q: 3. 1. Sdx 2. Sa+2 2x+1 dx x+1 3. S: dx x²+2x+5 1 4. Sdt 5. S dt 7t-1 (4-1 dt S 5-t3 6.

A:

Q: 2 3 dt. 0 1+t2

A:

Q: 8 2 f(x)dx -43, then | f(t)dt = If 8.

A: Given By the property of definite integral, we have

Q: dæ Evaluate: x/9x² +4 A) None of the above V9x² + 4 + 2 B f (x) = -2 ln +C %3D 3x © s(12) = -- In f…

A: I=∫dxx9x2+49x2+4=t9x  dx9x2+4=dtdx=9x2+49x dtI=∫19x2 duI=∫1u2-4 duI=∫1(u-2)(u+2)…

Q: 4 2 S[(x) dy dz 0 0

A:

Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

A:

Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: max z = 3x, + 2x2 1 1 X1 + 40 X2 < 1 60 s.t. 1 X1 + 50 1 X2 < 1 50 X1, X2 20

A: dual of the given lppmin z=y1+y2s.t.     140y1+150y2≥3      160y1+150y2≥2          y1,y2≥0

Q: 3- Suppose that s(x)dx 5. Find A- B- S V3 f(2)dz D-

A: Definite Integral of function f(x) in the interval of [1, 2] is 5. The function remains the same for…

Q: (1) If f(x) = { 3 x2 ; -1<x<2, then 0 ; otherwise compute [ xf (x) ]dx and [x²f(x)]dx

A:

Q: 1. [a+vPdz (1+ Vx)²dx 1 2 (x² – x) dx (x-1 3. + x)2 -d.x x2 4. x'dx x3 – 3x + 5 -dx 5. 3 2.

A:

Q: ex-4e-x ex 2 x-² / + C ex Option 1 dx 2 x + ² + C ex O Option 3 x+2 ex + C O Option 2 x-2e * +C O…

A:

Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

A:

Q: ydy 1. S- V25-16у* xdx 2. S- 9+x 2 dz 3. S- 2 +6z+10 xdx 4. S- 9+x

A:

Q: In the function given. Evaluate the integrals.

A: Given:∫03 fx dx=2,∫36 fx dx=-5∫36 gx dx=1∫36 3 fx -gx dx=?

Q: 1. F(x) = S t³ - 5t dt

A:

Q: 1. f(x) =x+6r-7x 2. S)=r-7 +2* 3. F(1) (1+7t) 2x+1 4. g(x)= x-1 1-4u 5. h(u) = 1+ 3u 6. H(s) = avs+…

A:

Q: 4х Compute dx Vx2+1

A: Given,           ∫354xx2+1dx

Q: 4. Compute (a)음(3e2-4) dx (b) 4 dt dx-x 1+t2

A:

Q: /1- 7y² dy

A:

Q: V1-x2 3. Evaluate S S /1-x²-y² dxdydz V1-x2-y2-z2

A: We will solve the following.

Q: x2 + 2x + 4 dx 3-Jx– 1)(x² + 2x + 1)

A: Convert rational function into partial fraction. And than integrate function.

Q: 10 F(s) s(s + 1)(s² + 8s + 15)

A: Given Fs=10ss+1s2+8s+15

Q: 2s - 1 s2 - s -- 2' F(s) = s2 – 4 - 4 F(s) : (s2 + 4)2 1 F(s) = s2 + 3s + 2

A:

Q: 2y – x = 3t y+ x' = 3et 3e-t x (0) = y (0) = 0 3s2 L (x) = (s+1)(s–2)(s²+1) 3(2s3 –s–1) s2…

A:

Q: Find the first and second derivative. S=4t^3-3t^4 Ds/dt= D^2s/dt^2

A: Explanation and solutions is given below....

Q: 9. xy(1+xy2) = 1 Ans: + y² -2 =

A: The given ode is xy1+xy2dydx=1 which can be written as dxdy=xy+x2y3

Q: 3 5. [20 points] Solve (x + y)dx+ dy=0 +x-

A:

Q: dx = 2x - 1 x³+3x + C x2 +C -- 3+C 2. 6. In x +C In x +C

A:

Q: -5 #2. Suppose that S„ƒ(x)dx= 6 andS²,g(x)dx= -4. Find S°,[3f(x) – 0.5g(x)]dx.

A: To evaluate the given integral apply the following rules.

Q: 2) 2yy' = x(1-2y). y(l) =1. Ans.: x +2y+ in(2y-1) 3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Vy2 -25 dy S y3

A:

Q: (-x+2, if – 1 sx<2 V3x – 6, if 2 < x< 5 -2x, if x <- 2 lx² – 1 , if x <- 2 1. f(x) = 2. f(x) = 3.…

A:

Q: 1. -(3X)(Px v Qx) 2. (x)(Sx• -Qx) ɔ (3x)Px | -(x)Sx

A: We have to prove the given arguments

Q: dx 4√/3x-x² 5³-

A:

Q: In Exercises 7–10, determine from its graph if the function is one-to-one.

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: 2 Find / U(x) + 4g(x)]dx if -5 2 2 | f(x)dx = 6 and / g(x)dx = -3. -5 -5 2 [f(x) + 4g(x)]dx = i %3|…

A: Given∫-52f(x)dx=6∫-52g(x)dx=-3