ek+3 1 f(x)dx=? k-1 If f(x+ k)dx=8, where k is constant, then А) 8 В) k-8 c) 8-k D) 8+k

Q: F(s) = (8s + 11)/[(s-4)(s²+9)] %3D

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Q: Vx/3+1 dx x2/3

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Q: ions: a). f(2) = ea %3D 22 +9'

A: As you have asked two unrelated and different, we shall answer first question only as per the…

Q: 7. - equations. solve the given equations using separable diff 1-4v² dv 6. x- dx ,when x = 3, y = 2…

A: The given differential equation is xdvdx=1-4v23v

Q: v² =v² +2a(s-s) i. j. K = = kx² 2 k. T = 27 е g ,a = ,X = ,g =

A: This question can be solved using the concept of explicit function.

Q: 3y + 2y Solving by variation of parameter y" Wronskian W is: 3e*cosx, the value of |

A:

Q: -3 -4 Evaluate: ₂₁ (4x²y - z³) dz dy dx

A: ∫03∫-24∫10(4x2y-z3) dz dy dx

Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: Q3/B/ Let X and Y are two r.v's with joint p.d.f 2x+y 2 2) =-------------------

A: It is given that X and Y are two random variables with joint PDF fx, y=2x+y210, 2<x<6 ;…

Q: %3D %3D = 7 and y = 7, find z when x = 3 and y = 5. Round your answer to two decimal places if…

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Q: x dy dx x² + y² = In /2 x² X´ + y

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Q: cx + dy - f(x, y) = ; P(3, 4); u =i+ x - y

A: Given that  f(x,y)=(cx+dy)/(x-y) P(3,4) and u=(4/5,3/5) To find the directional derivative of f at p

Q: s2 Y(s) : Find y(t), also what is y (0)? s3-2s2-s +2

A: Given :- Let Ys = s2s3 -2s2 -s +2 To determine :- find yt and the value of y0.

Q: fx,y (x, y) = Evaluate E[Y]X = 0.8] > given by [(x + y²), 0 < y ≤ 1,0 < x≤1 0, otherwise

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Q: s2 + 11s + 20 1-J = (1)h (q) (s² + 4s + 8)(s + 1)² J* %3D

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Q: Sf(x)dと SgCx)dx, suppeat 9 Explain why SfC dx 7 goa) Counter ekample to やU8e a your claim .

A: Use substitute rule unless the integral can be simplified and directly evaluated. Counter example is…

Q: 1. Let f(x, y) = Vx³ + y5. Find f2(0,0).

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Q: 2s +1 s2 – 2s + 2 7. F(s) = %3D

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

Q: Prove this equation by deriving F(x, t) =X(x) Y(y). Please show full steps OF OF 2. +2x- =D0 Ditebak…

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Q: 26. f(y) = y(2 – y), g(y) = %3D

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Q: Solve Fyy +3 Fy +2 F = -3 x, F (x,0) = x, d, F(x,0) = 0. ху F(x, y) =|

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Q: хр %3D S + X хр Find at (-7, 1) if xy: %3D (Rou

A: We have to find dy/dx   at (-7, 1)

Q: Ax) %3D х* — Лх2 - 12x where A> = > — Лх? — ЛЕx where ^> v that fis one-to-one on S = [- rmine f(S).…

A: Given, fx=x3-λx2-λ2x,  λ&gt;0

Q: 10 Let y = ( 2x + Then -A(2x + 10)" (2- 10)°, dy = A[ 2x + 2 - where A = %3D C = %3D

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Q: : + yz? + 2ry- = 0 ve z = f (r,y) ise =? what is the f(0,1) at O a. 1 O b. -1 O .0 O d. -2 O e. 2

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Q: | f(x) dx = -2, f(x) dx = -7, g(x) dx = 9, g(x) dx = -5, %3D

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Q: I(n) = ;n² - 글까-10 5-2t h(t) = t- 1 %3D S(h(0.5)) =

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Q: 6. 6. If f(x) dx f(x) dx = 3.8, find 5 f(x) dx. = 12 and %3D Answer:

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Q: (4x® y-18x² + y)dx+(x* + 3y +x)dy= 0

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Q: f (x) dx=6, ƒ (x) dx=2, and ƒ (x) dx=- 3, fir If A 4 B

A: We are asked to find the value of given.

Q: 3 6. уд + уi —D 1, when x %3D 0, y %3D 4 0, у %3D 4 dx

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Q: 3. The point Zo = 1/2+iis |Z| ≤ 1? point of

A: A point x0∈X is called an interior point of X if there exists an open ball B(x0,r) centered at x0…

Q: If y(#) = and z increases from 0 to 0.5 then dy = 0.5. %3D %3D 1+ *

A:

Q: x²-x=1 1 x(x+2)3' Solve for f: using (a)Trapezoidal Rule (b)Simpson's Rule. Use n = 10 (c)Boole's…

A: To solve the integral using the Trapezoidal rule, use the formula ∫ydx=h2[y0+yn+2(y1+y2+…+yn-1)]…

Q: а) у%3DIn(x? + 4)(2х + 5) b) у%3DIn (12х - 7) с) у ex2+3 ex-4 - d) y= 2x'ex e) y = ev3x+T

A: Given data:   a) The given function is: y=ln(x2+4)(2x+5).   The expression for derivative of the…

Q: 25. f(y) = y?, g(y) = y + 2 %3D

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Q: 53 what is 13' 3 Given that f(x)dx = f(v)dv?

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Q: r (5) r) 6Г (2.88) 2- r(-2,5 )r (4) 1- 3- ЗГ (088) r (2)+ r (3 ) 4- e-** dx 5- S Vy e-y* dy

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Q: etermine whether the following statements are true or false and justify your esponse. -3x d²y dy y =…

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Q: (c) y = 1, y = 1/2, x = 2 (d) y = √x, y = 22, x=9 (e) x = 2y², x = 4 + y² (f) x = 1 - y², x = y² – 1…

A: The area between any two curves is given by formula A = ∫ [f(x) - g(x)] dx  with limits from a to b…

Q: 5. For what value of k, k> 0, does (6kx-2k) dx = -k³ ? о 1 02

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Q: bah ow )o (d) be . Solve for 0<x <1, u"- u =-f(x) u' (0) = u' (1) = 0.

A: As f(x) is an arbitrary function, we will use Green's function to find the general solution.

Q: 2. V9 – y?, y = 1, y= 3, x = 0, about the y — ахis -

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Q: (ii) y" – 4y' + 4y = e3", y(0) = 0, y'(0) = 0. %3D

A: We have to find general solution of the given initial value problem.

Q: '0- DXJ 1- E K 2- DxF 3- Show that A×C÷C×A

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Q: 6x + 6 13 dx Evaluate - x4 -3 О З2? + 2 - 13x + C, Where C is the parameter O 3x2 – 2 3 – 13x + C,…

A: We have to find

Q: S(3x².fu)+x°, f'(x) dx =24 so, so, f(2) = ) %3D

A: We have to solve the given question. Derivative of the function f(x) can be written as f'(x) Product…

Q: et2-2 2.2 R dxdy, where R between x2 = -y, y = 0 and x = -3 , y = -9 %3D

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Q: 10 Q5/ Evaluate x*dx ,n 5, using trapezoidal rule.

A: The trapezoidal rule formula is: ∫abf(x)dx≈∆x2f(x0+2f(x1)+2fx2+...+2fn-1(x)+f(xn))...(1) where,…