21 11 f(x) dæ f(x) dx f(x) dx - 8, where a = and b ...

Q: Ex. Find the general solution to dy 1 -2.x dx X -

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Q: 3. Evaluate: 12x dx (a) J2 2-1)* (b) F sin 20 de o cos 20 (c) L1; x2 dx -1 x+2 (d) S, 2x Vx2 + 2 dx

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Q: 1-X 1.S.S C14 X) dY dX (1-x) dy dx 1+X

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Q: 1. IT (2, 4) dar dy =/| f(x, y) dy dx %D 0. 0.

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Q: dy (2) Find at x =-1 if y = u³ + 5u – 4 and u = x2 + x dx

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Q: (a) ſ x sin(2+ x²) dx (b) Sí Зи du u²+u–2 (c) ſi z dx 2 x²+x+7 (d) * x²e-3x dx -Зх

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Q: 1. Classify the D.E. 2xe dx + (x²e + 1)dy 0.

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

Q: 1-x -x? dy dx -1 J-V1-x² (1 + x + y)² X.

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Q: 18 12 | f(2)dz – f(2)de = f(x)dx | f(x)dx 4 where a = and b =

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Q: 21 11 | {(=) dz f(x) dx = where a = and b =|

A: Given: ∫821f(x)dx-∫811f(x)dx=∫abf(x)dx   We know that ∫acf(x)dx= ∫abf(x)dx+∫bcf(x)dx We can write by…

Q: 25. What is the y' of y = tan(6x - 5)? a. y' 6csc2 (6x - 5) b. y' = tan(6) с. у' %3 6sec? (6х - 5)…

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Q: x²+x-2 J (x2–1)(2x-x²) dx can be resolved into dx dx. + DS x-2 dx dx.. A x- х-2 dx x+1 x+2 - dx do.…

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Q: 17. (бх - 2у + ye")dx + (хе" - 2x)dy 3D0 19. (у? + ysenx)dx +(у+2хy- сos x)dy 3D 0 21. (2x-e' + ye*…

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Q: 15. /7.- dt 16. x+ 3 dx P + f - 21 2r - &r

A: Solution:Given      ∫dtt3+t2-2tFormula:∫dxx=log x+C

Q: If y = e Oe3 Oe 3x X² O 2e3 O 3e³ then dy dx at x = 1 is

A: To find derivative of given function at x=1

Q: 1. Find -for each of the following: dx e) y =x* Inx f) In(x + y) = e*=y g) y = x2r-5

A: Here we have to find dy/dx .

Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

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Q: 18 12 f(x) dx – | f(x) dx = f(x) dx - where a = and b =

A: Find value of a and b.

Q: 26. (2xy2-3x²)dx + (x² + 2y)dy = 0 A. Exact B. Not Exact

A: As, the student has posted multiple questions but we can solve one question at a time according to…

Q: 1. Find dy dx S(x)= e**/2x-5 (6-5x)* (iii) f(x) =

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Q: 4. If ( Inx dx = f(x)[In(x) + 1] + C, then f(1) = A 1 B D -1

A: Solution

Q: 7. Find: y = In dx √6x-5 [ Lex (x+1)³.

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Q: 27 18 f(x) dx – f(x) dx = f(x) dx where a = and b =

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Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: 17. If y = x, then dy/dx (a) x²-² (b) x²-1 lnx (c) x²²(1-In² x) (d) x²-²(1–In x) (e) None of these

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

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Q: dy 6. Determine for dx In( xy) + x² – xy 2 -1 e +1

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Q: 1) In this problem, let * = 2, the value Ar = dx, dy = f ' (x)dx, and Ay = f(x + Ax) - f(x) to…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: 23 14 f(x)dx – ¹ f(x)dx - - where a = = b [ f( and b = f(x) dx

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Q: 18 10 f(x) dx | f(x) dr = f(x) dx where a and b

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Q: find dy/dx of the following:

A: Please refer to the image below

Q: 18 13 f(x) dz - f(x) dx = f(x) dx where a = and b =

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Q: 8) a) Find dy/dx if: e3x = x+y b) Differenctiate y = (sin r)"

A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

Q: -11 If " f(x)dx = 1 ; S,f()dx = 22 find f" fx)dx. Eiles

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Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

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Q: 4-compos dx dy 5-find dry if f(x, y) = xe xe 6- find (x²³/2)

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Q: .5 If f(x)dx 4 and | f(x)dx =7, then f(x)dx = %3D

A: Answer is below

Q: 21 13 f(x)dx – f(x)dr f(x)dx where a = and b

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Q: 1 1 Evaluate f dz[ dx [ e dy. бе/3 (бе-б)/3 О бе-6 6/3

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Q: 4. Compute the following: (a) e dx -1 d (Ъ) dx f'(x) dx a

A: 4.(a) The objective is to find the value of ∫-11edx

Q: 1 1 Evaluate f dz dx f ez dy.

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Q: -2n f) S“ cos 2x dx g) S et² t dt h) S x sin(x²) dx

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Q: 42. a. Find df /dx if f(x) = 2 In. dt. b. Find f(0).

A: Solution is given.

Q: 1. Find dy/dx. 2.3 (a) x²y° + cos y = 0 (b) x – 3.xy + y³ = 5 -

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Q: 2 Z - 6 A xy dy dx dz 3.

A: ∫03∫09-z2∫0xxydydxdz

Q: 13 12 f(x) dx – I s(x) dx = f(x) dx where a = and b =

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Q: 2. Find b such that dx 1+x2 3

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Q: 4. If x = 1+1 & y==1-t² then dy - at t =1 is dx а) 1 b) 2 c) -1 d) - 2

A: Value of dy/dx at t=1 is