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Q: Rewrite c(x) = (x ^ 2 + 5x + 2)/(x - 3) in the form y = q(x) + (r(x))/(b(x)) has degree less than b.

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Q: -2 -4x S so*x²dydx

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Q: 2x-1 Find f1) if Az) = %3D x+2. a) O b) O c) O d) 515

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Q: r (1-x)²dx x3/2

A: Given: ∫(1-x)2x32dx

Q: b. Маx z %3DX1 + X2 s.t. 2x1 + x2 < 20 X1 +3x2 < 15 X2 < 4 X1, X2 2 0

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Q: If y(x) =2ke^(-2kx) for x>0 , then (x) = %3D

A: We have to solve given problem:

Q: In the given question , find d2 y /dx2implicitly in terms of x and y :- x2 y - 4x = 5

A: Given that, x2y-4x=5

Q: III Find y" if y=2x- 4x-x²+7 120x -24 A O B O x² - 4 120x+24 D. x²+4

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Q: Q2 :If A = 3i + j- 2k B = -i + 3j + 4k Find, 1- A +B 2- 3A - 2B 3- A x B 4- 0(A,B)

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Q: -x + y2 = 3 and x + y2 - y = 0

A: Consider the given equations as,

Q: -x + 2y 3 %3D 4 II

A: Given the equations x'=dxdt=-52x+2y                         (1)y'=dydt=32x-2y…

Q: а)у-x^3-5x+5 b)y= xe^X с) In(x^3

A: # we are entitled to solve 3 subparts of one question. Please resubmit the question which you wish…

Q: 70. 4y" +5y' - 2y = e²+xsinx

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Q: Use Cayley-Hamilton to find B4 and B-1 . Where [1 B = 0 1' 1 - 3 -1

A: It is given that B=12-101-13-11 The characteristic equation is given by:…

Q: 10. Complete the table on the right assuming that: y-4x+2. 6. 18

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Q: a'+3ab? If 3a’b+b³ 3x°y+y' _ x³+3xy² X_ y Prove that a b

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Q: What is? 2x-1=y,2y+3=x

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Q: Find the term of (a-2b)^13 that has b^3 in it.

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Q: x² + 1 If y then y' will be = 2x – 3ex'

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Q: f(x)%3D4X+4,g((x)3D4×+6 -(x)(B+)¯0

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Q: z) if - 11z - 75 | and g(x) %3D T2 + 10x + 2 separate your answers.

A: We have to find the value of x according to the given information

Q: = x²e2= 2x- %3D nd

A: Partial differential eq: w=x2e2x+3yWe need to find ∂w∂x|(1,0)

Q: 8. . x² = 4y and y %3D x2+4

A: As per the guidelines I can solve only first question

Q: Tpy and B= -1 x² + x² + y² + 1 A<B

A: We have,  and,

Q: Find x, and x2. - 5 1 6- 15 -2 3 X2 - 3 17 X1 %3D X2 =

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Q: —2ху y' = x2 + y2 у(1) %3D1 [2

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Q: Find AB. A 5x B] 4х + з с AB %3D 5

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Q: Show-= x2 y2 = 1 is r² = b2 a2 b2 1-е2 сos2 0

A: To show  x2a2−y2b2=1 is r2=−b21−e2cos2θ

Q: Find x and y in terms of a and b. ax + by = - 5 bx + ay = - 5 %3D

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Q: if X-? yk 2 2 3D5 リ+1 yX Find

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Q: Q3/ If Ā = -3i + 2j + 5k, B = i + 2j - k and C = -i-j-2k %3D find (AXB). C

A: Let's see the concept of dot and cross product. Say xi+yj+zk and ai+bj+ck be two vectors.

Q: (b) x²d²y dr2 dy + 16y = 0 + 9.x- dr

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: (b) a²y" – 4xy + 6y = x², x > 0

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Q: 2х — 7у — 9z %3D-16. y +s +t

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Q: If y3 – 3ax? + x³ = 0, then prove that y2 + 2a?x?y-5 = 0

A: The proof is given below :

Q: f(x) = 2x(3-x2) x²+9 %3D as x → -∞

A: Solve the given limit as,…

Q: Find y' for y = 8x-3- 9x-1 - 9x -1 y' =O %3D

A: Differentiate y with respect to x  using polynomial rules

Q: AB is a midsegment of AXY Z. If ZB 3p-4 and BX = 2p+20, what is the value of p? %3D %3D A Зр — 4 2p…

A: For the given Triangle XYZ  AB is the mid segment  ZB = 3p-4 BX= 2p+20 p is calculated as shown…

Q: [3x-Y3D2 6x +2y =16

A: 3x-y=26x+2y=16

Q: EXAMPLE: FIND a2z a?z a2z AND дx2 дудх 7. z = 3x²y3 – 4x*y?

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Q: (r² + y² )²dydx • Evaluate:

A: Given: ∫03∫09-x2x2+y252dydx

Q: For A = 2ax + 3ay + az and B = 5ax - 2ay - az OAB is:

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Q: Find (axb) x c if a=i-2j-3k, b=2i +j-k, Q2. c=i+3j-2k.

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Q: B (m,n) = xm-1 (1-x)"-1dx %3D

A: Using the definition of Beta function  Bx, y=∫01tx-11-ty-1dt                  1

Q: to the right of z= -2.17

A: We have to find area to the right of z

Q: 5. (2xy² – 1)* – 3x²y³ – 1 = 0, find y' -

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Q: 3+ 6x 5x + 12 Find x if BC = and XC = %3D 10

A: Given,            BC=3+6x5 and XC=5x+1210            The figure is shown below :           To find…

Q: the area to the right of z=-2.26 is

A: The normal distribution:A continuous random variable X is said to follow normal distribution with…

Q: Shon in Question 1.a find your mista y= -2x + 1 y3 -2x +3 y 2. -

A: