47. f(x) = 3 48. fx) — х 5 49. f(x) = x² + 1 50. f(x) = x² + x 51. g(x) 3D х3 +х 52. g(x) = x* + 3x? – 1 х 53. g(x) x2 54. g(x) : x2 55. h(t) t 56. h(t) = |r³ | 57. h(t) 2t + 1 58. h(t) = 2|t| + 1 59. sin 2x 60. sin x? 61. cos 3x 62. 1 + cos x ||

Q: 21. Кх, у) 2х -у ys 4x + 6 5 * 4y s 7 2r + ys7 бу X-6y z 10

A: Step-1 f(x,y) = 2x-y            y ≤ 4x+6 ⇒ 4x-y ≥-6            x+4y ≤ 7           2x+y ≤ 7…

Q: .3 2- S(y² – 4y + 2 ) dy

A:

Q: 1 max z = 2x, + x2 - x1 + x2 s 1 Xị + x2 s 3 s.t. 2x2 < 4 X1, X2 2 0

A:

Q: Find the general cowtion of the die. y9) + ya) - 24 =-e (9+67x+17 x²) + (861nax - o cosex) „(2).…

A: The given differential equation is , y(3)+y(2)-2y = -e3x(9+67x+17x2) +…

Q: write each of the following sets by listing their elements between braces. Please show work.

A:

Q: Max Z = x1 + 3xz+ 4x3+ 5 S.t. 4x1+ 3xz+ 2x3 +x4<10 X1 – X3+2x4= 2 Xj+Xz+X3+X21 X1, X2 ,X3, X2 0

A: Phase 1: The Given problem is converted to canonical form by adding slack, surplus and artificial…

Q: If it is known that L {y'' (t)} = -15s+24 with y(0) = -3 and y'(0) = 6, then it can be ensured that:

A: The given problem is to find the Laplace of y(t) from given info, given Laplace of y"(t) =-15s+24…

Q: 2. a) Use the Trapezoid Rule to estimate the value of: [V10-7e-03x dx. Letn=6. x |f (x) Round each f…

A: The equation for calculating the integral of a function y=f(x) by trapezoidal rule is; I=∫x0xny…

Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

A:

Q: Max z = x1 + x2 s.t. 2x1 + x2 ≤ 20 x1 +3x2 ≤ 15 x2 ≤ 4 x1, x2 ≥ 0

A:

Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

A:

Q: ことる ーx (x+2)(X-2) -6x (x -ax+4) y" CX+2) (x-1)3 need first derivative Eanalysis %3D (x-2)3 (x+2)°

A:

Q: - r)rdrde 32(V2-1) 16(VZ-1) c. VZ-1) 4(VE-1), S(V2-1) a. d. 3. 3 3 e. 3.

A:

Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

A:

Q: Differentiate y = In(x³ + e*) .2 3x+eX А. x3+e-X 3x2-ex В. x3 +e-X 3x2-e-x C. x3-e-X 3x2-e-x D.…

A:

Q: 8. = In(3x² – 2y + 4z³); x = 1/2, y = t²/3, z = 1=2 w

A:

Q: x) = "1 U2 (t) y(1 [1 – 2e-(1-2) y(t) = 2 "20 1- 2e-(-2) + e=26–2)] + 10e- – 7e-2t -2(t- y(1) = 21-…

A:

Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: Evaluate S ( + - + e²+ =) dz 3 · 3z 21² In x++²x+}x+ + C Option 1 √√(x³)x= √√√x + √2x+C I- Option 2

A:

Q: 1. Find all critical points and investigate the type and stability of each. x' = xy - 2 y' = x - 2y

A:

Q: how would I take the partial derrivitive of this equation, I cannot use the chain Rule as we have…

A: Given function,

Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

A:

Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

A:

Q: Solve y′′(t)+2y′(t)+2y(t)=H(t); y(0)=1 ;y′(0)=0 where H(t)=2t+3 , 0≤t<1 H(t)=3t+1, t≥1

A:

Q: y = x(arctan x)² arctan (x+ (1+x²)arctan x) А. 1+x2 arctan (2x+ (1–x²)arctan x) В. 1-x2 arctan (2x+…

A:

Q: Jy > -x² + 6x – 12 ly -x² + 6x – 12 ly>x² - 4x – 1 Sy -x² + 6x – 12 Lyzx? - 4x – 1 Syx² – 4x – 1…

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: How would you interpret the coefficient of β2 in each model? Ln(Y) = β0 + β1 Ln(X1) + β2 Ln(X2) +…

A: Note : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: 2. If a runner traveled a distance of d(h) = v16h4 in time t(h) = 3h – 3h - 5h2, what is the…

A: We will find the distance as following.

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: 4. y=6-ax-x", y = x+l6, about the a %3D | yaxis

A:

Q: the differential equati x²y' – 2y = Inx² is cje2* + c2e¯* – x + 5 O c1x² + c2x=1 – In x + ; O 2 +…

A:

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

A:

Q: 10. Solve: (2st +1 kds – 3s° dt = 0, s(-1)=1 a. 8st' = (s -t) – t)² c. 8st = (t – s) 3 а. 8st3 b.…

A:

Q: 9 2. If fS(x)dx= 37 and g(x)dx=16, = 16, find [2f(x)+3g(x) ]dx- %3D 0.

A:

Q: 1) If h(x) = x³ +1, find h-'(x). (A) h-'(x) = 3+ (x +2)³ (B) h-(x) = Vx – 1 (C) h-(x) = 2r³ – 3 (D)…

A:

Q: 9. The total cost and total avenue, in dollars, from producing x couches are given by C(x) = 1000(x²…

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: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: 2* If ODE of 2nd order and y. 2 x + 3 e-2x, the suggested y, is: C e2x + c2 e3x Yp = Yp = a, x + a2…

A:

Q: dy Ify드a2-4x-의. then. dx x2 2x-2) 2-4x-5 einz2-4x-5)- In(z+2)]. x2-4x-5 x2 x2-4x-5 x 2 x 2 2-4x-5…

A: Consider the given equation:

Q: x²y-y -y': у+1 ; у(3) - -1 %3D а. х3— х — Зу- Iny3 - 21 %3D с. х3 — Зх - Зу- Iny3- k d. x3 - 3x -…

A: Given that : y' = (x2y - y) /(y+1).and y(3) = -1. We solve this differential equations by using…

Q: Number 29. Find the derivative of the function. I'm confused with the simplification part at the end…

A: Obtain the derivative of the function as follows.

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: If we use the secant method on fx) = x+x+3 with x2 and X-1 = 1, then X, is

A:

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

Q: /25-22-y2 zVx² + y? + z² dz dy dr

A:

Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

A: