(ii,if i = j A =, if i +j if i # j ((i B = + 1)',if i = j j+1'if i # j

Q: by first- shifting find L(t2 e-3«) = %3D (s+3): ; * 0 a O (s+3) 2 * b O 3.cO (s+3) 3 1

A: Solution:- Correct option :- a Detailed explanation

Q: _11. What is Sdx? A. +C B. +x + C х-1 C. c. ++ 2x + C x(2x2+3x+6) + C x3 D. _12. In solving S th dx,…

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Q: 4. 5 Show that if y%= x+4 then dx (x+4)** %3D %3D 16. dx. 2 (x+4)² **n Hence, find the value of|

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Q: A tank, with a capacity of 200 gallons, is half filled with distilled water. At the instant t= 0, a…

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Q: In VVi+1-2 dt, if we let V Vt+1 – 2, then dt is equal to A 2(x²+2)dx ® 4x(x²+2)dx c) None D…

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Q: 4. Solve the equation satisfying the conditions: dt ax (i) T=0 when x= 0 and 1 for all t 2х, 0Sx<1/2…

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Q: 5. (5 – x)² * 6 Show that if y=3-x then %3D 6. . (x-s) _ xp 1. dx. 3 Hence, find the value of , 2(5…

A: In differentiation use quotient rule In integration use substitution

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to A (4x³ + 2) dx B) None 2(x²+2)dx D 4x³dx 4x…

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Q: 4. Ifu = f(x), then : dx = J x* + 2x² + 1 k + C for some constant k. x² + 1 Compute kf (1). (a) ¼…

A: The given integral is ∫xx4+2x2+1dx=∫xx2+12dx To compute kf1

Q: dx 4. J xV25-x2 a. In 5+Vx2-25 + C 5+Vx2-25 b. In + C 5+v25-x2 In + C с. d. None of the above

A: In this question we have to solve given integral.

Q: 1. S(Vz5 + Vx ) de с 6 x2/7 +- 2. x5/6 +x³ +C 1 x3 + C 1 7/2 x3 + C х6/5 + - х3 + C + - O A О в O c…

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Q: 14. Find X(s), given x" + 16x = t, x(0) = 0, x'(0) = 0.

A: answer is in next step

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: For z > 0, 옮(1 In (t³ + 1) dt A) In (x³ + 1) B) In (8z³ + 1) c) 2 In (z³ + 1) 2 In (z² + 1) D) 2 In…

A: Solution: Consider the given that; ddx∫02xlnt3+1dt We have Leibnitz Rule: ddx∫a(x)b(x)f(x,t)dt =…

Q: In t+1-2 dt, if we let t+1-2, then dt is equal to A 2(x2+2)dx (в 4x³dx O 4x(x2+2)dx D None E…

A: Option C is correct.

Q: Suppose that for a 2 x 2 matrix A, AŬ= 3õ for ū = How is the pair (3, v) called for a matrix A?…

A: given a matrix A of order 2×2 ,  Av→=3v→ for v→=-1-1 (a) how is the pair 3,v→ called for a matrix A…

Q: For ſ k*e3* dx = 1 (ke)3x 3 (1–In 2-1) + C. If u = 3x, then k =?

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Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

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Q: 10. Solve 0sxSa, 1>0 subject to the conditions dt ax O (0, 1) = 0 (a, t) =0 and 0(x,0) = 6,…

A: 10. Given partial differential equation is∂θ∂t=∂2θ∂x2 with initial conditions…

Q: function is given by: f(x)1 − 4x cos(x) + 2x2 + cos(2x). Find the solution of f(x) = 0 within 10-5…

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Q: f(t) = e3t + cos(6t) – e3t cos(6t) As4 + Bs3 + Cs² + Ds + E F(s) Fs5 + Gs4 + Hs3 + Is² + Js + K

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Q: 12. Solve the problem: Utt = c*upx + Ax, 0 0, A= constant, и (х,0) — 0, и (0, t) — 0, Ut (x, 0) =…

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Q: kx 4+x² If k > 1, evaluate O ka -In|x² + 4 +C 2 Okx -arctan (2x) + C 2 Ok In(x² + 4) + C O arctan…

A: Given: I=∫kx4+x2dx   ...1   As we know the common integral. ∫1ax+bdx=1alnax+b+C

Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: Find the Solution (1+r)ds + 2sr-3(1+r)dt = 0; when t - 0, s = 2. ® : (1 - P12-e* ®= (1 - s12-e © : =…

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Q: 2. J고dr (e* -1) (e +1)

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Q: I(x) = /, (In(t))² e-(t-1)* dt - 3x

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Q: 2) Suppose A is a constant such that Ae2a is a solution to the DE y' + 4y + 3y = e2a. Find the…

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Q: d [e'- In (21+1)]dt, find g(x) . dx -2 A ex-In(2x+1) 2 B ex_ (2x + 1)2 4 C (2x + 1)² 4 D (2x + 1)²…

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Q: If f(z) = z - 173 = 0 then the iterative formula for Newton-Raphson's Method is given by Pa =?

A: The iterative formula for the Newton-Raphson's Method is given by:xn+1=xn-f(xn)f'(xn)

Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

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Q: Find the largest interval on which the LV.P (x +(4) x -5) y" + sin(x) y' + y =0, y(0)= 3, y'(0)=4…

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Q: 9(x) = J(z) = と (-1)" (n!)2 X 2n n=0

A: We take first and second derivative of given then adjust the summation.

Q: 7- f (x)= 3.x², 0<xr<1 olarak verilsin. P(/2/ (2, = ? O a. 1/8 O b. 1/4 Oc 3/4 O d. 7/9 O e. 1/9

A: Solution: 7. From the given information, the probability density function of X is

Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to 4x(x²+ 2)dx B (4x³+2)dx None D 2(x²+2)dx E…

A: To find out the dt.

Q: 1 d) 2r- dz - r e² – e-z e) J ez +e-z° rp- In 3 f) 1 ez +e-z Ip-

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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.…

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Q: Also p; 2 0 for all j = {1, ., k} and E-1P; = 1. What is the value of E(X) and V(X)?

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Q: The solution of * x² +3y² dy/dx= 2ху In y=In (1+y^2/x^2)+C none of each other O x= (1+y^2/x^2)+C In…

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Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

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Q: 7. Find the general solution to y" + 2(x – 1)y' + 4y = 0 using an integrating factor of the form ax…

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Q: d If g(x)=- S* [e²-In (21+1) ]dt, find g(x). -2 2 (2x + 1)2 4 B (2x + 1)² Ⓒe-In(2x+1) 4 (2x + 1)² di…

A: A function is given by, gx=ddx∫-2xet-ln2t+1dt. The objective is to find the second derivative g''x…

Q: J o とツ(x)心 り(- ニ 2) n (x) +In (5+x) = 2 Ino 3)\oy (メ-7) 2 5

A: Simplify the given expressions

Q: Part 2 of 5 Integrate both sides and use the power rule on the right side. 5+1 y = 48. + C 5+1 6 8 +…

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Q: Find the general Solution For thhe Fouowin Gy 3yorem oF FイのヒーOrder di F Ferential equationj. linear…

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Q: The Newton-Raphson method fails if Of" (x₂) = 0 Of (1₂) = 0 O f' (1₂) = 0 0 = (º¹),f O

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Q: 3) Find the general solution by using reduction of order method to ty" – (t + 1)y' + y = 0 given…

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Q: (x, y) - arty! - b where x is the amount of money expended on labor, y is the amount expended on…

A: Solution is below

Q: 7. Solve the following first-order linear DE's. y' + (cotx)y = xcscx, y = 1 8. Solve the following…

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