1. У (x2 + x3)4 9. У ln(x ln x) 1 + t 21. У 3x1n х 23, y = (1-x-1)- 25. sin(xy)-x2-y 27. y-logs 2x) 29. y--In sin x--sin-х 1. yan (4x) 33. yInsec 5x + tan 5x 35, y = cot(3x2 + 5) 37. y=sin(tan-/I +x3

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

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Q: B.S(cos x + cos 5x)dx D.S(cos x – cos 5x)dx A.S(sin x + sin 5x)dx C.S(sin x – sin 5x)dx 8. S sec³x…

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Q: 18. Evaluate ſe3 cos 2x sin 2x dx 1,3 cos 2x + C c.e3cos 2x + C B. -e3 cos 2x + C e3 cos 2x D. 6 sin…

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Q: 3.2 Differentiate 3.2.1 y= x¹ tan 3x. 3.2.2_y=ln(2x²+1). e +1 3.2.3 y=- -1 the following with…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Show that given differential equation dy y cos x + sin y + 9 – 0 is Exact and dx sin x + x cos y + x…

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Q: Differentiation#11

A: We have

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: Evaluate the following limits

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Q: Use integration formulas to solve each integral in Exercises  You may have to use algebra, educated…

A: NOTE- AS WE ARE ALLOWED TO ANSWER THREE SUBPARTS IN ONE SESION, SO, I HAVE ANSWERED FIRST THREE…

Q: 10. | [3 - e-lxl – cos x + log(x²)]dx = 0 x³ +4x – sin x 11. x² – 7 -dx 3 0

A: 10. ∫a53-e-x-cosx+lnx2dxEliminate absolutes =∫a53-e-x-cosx+lnx2dxApply the Sum Rule:…

Q: | cos(5x) sin(13x)dx = 1 sin(&x) ) sin(18x 4 6. OB. - 5 sin(5x) sin(13x) + 13 cos(5x) 1 cos(1&x)…

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Q: y = In(cos 3x) %3D 1 (- sin 3x)(3) Cos 3x y' %3D y' = 1 (- sin 3x) cos 3x 1 y' = (3) sin 3x %3D -…

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Q: 4. If y3 +x³ = sin y + sin x find. dx 3y²-cosy А. cos x-3x2 3y2-cos y В. - cos x-3x2 cos x-3x2 C.…

A: Given: y3+x3=siny+sinx To find: dydx=?

Q: Q#( 1b Compute: [cos (10x)sin²(10x)dx 1 sin°(10x) – A) 30 1 sin°(10x)+C 50 1 cos°(10x)- 1 -cos…

A: We have to solve the given indefinite integral

Q: ーズ ず+2+4= 8x°+ 12€ (10 +2y+4y = 10 Sin 3X 42デ+44- gSia2x

A: As per the guidelines I have to solve only first question. So for more solutions please repost the…

Q: 1. ƒ(x)=x²- = x² - secx 2. w = ex²-x² + 4x 3. h(z)=In(2z)sin(2z) 3x² 4. y= √x² +1 5. y³ + 2xy = 3

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Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: [ 2x sin (4x)dx O =cos (4x) + C -x² 4 2 sin (4x) + 8x cos (4x) + C sin (4x) – x cos (4x) + C ○중cos…

A: Integration by parts

Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

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Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: Find y' in y=sin¹ (5x5+2x) + Tan-¹ (x²) 1 1 1+x² -(5x5+2x)² A. y' B. y' C. y' D. y' = = 25x¹+2…

A: Given:y=sin-1(5x5+2x)+tan-1(x2)       y'=dydx=dsin-1(5x5+2x)+tan-1(x2)dx…

Q: 2. Suppose that a certain population obeys the logistic equation dy dt ry (1 - *) k (a) If the…

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Q: Find L{(1 – t) (3 + 2 sin 5t)} . 3 2s 10s - 82+25 (s2 –25)² - 10 20s 을 + - - s2+25 (s² +25)² 3 3 10…

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Q: | -3x cos 4x dx A) - 16 3 cos 48 -x sin 4x + C 3 3 3 B) cos 4x -x sin 3x +C 16 3 cos 4x - 16 3 C) -…

A: To evaluate the given intgral.

Q: 2. +4y= sin(3t), y(0)=2, y'(0) = 0

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Q: sin(6x) cos(4x) dx = sin (2x) sin (6x) (b) 글(s сов (2х) cos (6x) 2 o+( cos (2x) cos (10x) sin (2x)…

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Q: f(x)=X +Sin -1 く(-2)- 4-て+Sini-て)-\no9651 3(x)=てメ+ cosx ずし-て) ニ -4ACOS(-て)-3 (x)-2-らinx f(-2):…

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Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

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Q: If G= ex Cos y log z + exyz Cos(xyz) Tan y - log (Cos x3) solve ∂3G/∂x2z

A: Given, G=excosylogz+exyzcos(xyz)tany-log(cosx3)

Q: If y = (3x²+5) (2x³ - 5x – 4) then dy/dx O (3x2+5) (6x² - 5) + 6x (2x3 - 5x - 4) O (3x2+5) (6x² - 5)…

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Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

Q: Find L{(t – 1) (2 – 5 sin 3t)} . O 2 5s 30s - 82+9 (s2 -9)² 2 15 15 - - s2 (s² –9) $(s2-9) 15 15 2…

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Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: S sin x coszxdx = cosix + c cosix + O Option 2 O Option 3 -cosix + e -cosix + c O Option 4 O Option…

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Q: sin(6x) cos(4x)dx% = %3D (b) ÷( + ) Nin (6x) cos (2x) COR +c 2. 2)+ (e) None Cos (2x) Cos (10x sin…

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Q: on - Homogenous: To be considered Homogenous, the differential equation must be equal to ependent…

A: We are asked to find the  non homogeneous second order euqation.

Q: 4: ystem of differential ec

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Q: 4. [(3sin 2f – 3 cos 5t )dt 5. sin x dx cos x

A: 4) Given:            ∫3sin2t-3cos5tdt       =∫3sin2t dt-∫3cos5t dt taking constant out…

Q: 35) y = -4 sin x 4+ 2+ 2n -2+ -4-

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Q: x2-1 7) lím x--1 x+1 (x+4)ln(x+6) 8) lím x--4 9) lím x-0 Vx+5-V5 x2-16

A: Compute the limit as follows. limx→-1x2-1x+1=limx→-1x2-12x+1=limx→-1x+1x-1x+1…

Q: 1- LS7 cos(y)esin(y)+9x dydx 2

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Q: What is the general solution with steps of the differential equation y’=sin(3x)y+y+sin(3x)+1

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Q: 6. S cos 4x cosx dx will yield B.금sin Sx + 등sin 3x +c А. sin 5x + sin 3x + C c. 글cos 5x-글cos 3x + C…

A: Note: As per company policy we should solve only one question. So kindly repost the other questions…

Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…

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Q: 6x² + 5x + 16 S x3 + 3x² + 2x + 6 5 Injx+31+ In (x² + 2)√2 tan ¹() + C Option 1 5 Injx +31+ In (x² +…

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Q: 2. A differential equation that is a function of x only O will produce a slope field with parallel…

A: Here, given that the differential equation is a function of x only. So, dydx=f(x)⇒y=F(x)+C, where…

Q: 16. √(16-9x²) dx 17. dx/ (9x² + 4) 18. sin³ x cos x dx 19. f (secs x) dx/csc x 20. Stan² x dx

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Q: 6. Vsin x sin 2xdx Vtan 4x 7. J cos² 4x 8. cos 2xsin 2.xdx |arctan(3 – x) - dx 9. 1+ (3-х)? 3e 2y…

A: Given

Q: y" + 2y' + y = −e* [(− x² + 4x+3)cos x + (− x² + 4x + 3)sin x]

A: As per the question we are given a second order linear non-homogeneous differential equation. And we…