efe* cos 2t dt 1. 5. e 3 sin 2t 9. t S* sin at dt 2. 6. e' - cost 10. t e 3t | tsin 2t dt 1- cos 3t 7. 3. sin 2t 11. e 3t t t Sce* sinze dt e2t 8. -3t 4. 1 -at cos bt 12.

Q: s sec(cosx) dydx siny

A: Given : ∫01∫sin-1yπ2 sec2(cosx)dydx

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Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: - (Ax + B) - Ar + B where A = acz and B = bez. When i--a 0, the differential equation becomes X* +…

A: By using relationship between trigonometric, hyperbolic and exponential functions you can solve the…

Q: 1. [ (6x² – 2x+3)dx sin(2x)dx 3 2. 3. S2 8 dx X+2

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Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

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Q: find /x – x² - dx xV4x – x² dx 9. 10. х dx dx 11. 12. xV7 – x² xV7 + x² Vx² (4 x² 4 dx 13. 14. х sin…

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Q: 5z² – VE 1+ tan(x) Find an dy when y = dr Do NOT simplify. expression for

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Q: I don't know how to find d^2y/dx^2 for x cos y = 0. Do you implicitly differentiate the equation…

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Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

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Q: 1) The vertical distance y traveled by a falling parachutist can be computed by solving the…

A: The vertical distance y travelled by a falling parachutist can be computed by solving the following…

Q: 5 sin“(3t) dt

A:

Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: A ball of mass 4 kg is placed at the lower end of a vertical spring, whose constant of restitution…

A: To solve the nonhomogeneous differential equation use the undetermined coefficients. Negative…

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

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Q: dx (2tx +x+ cos t) + (-sin x +t² +t)- = 0. dt %3D

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Q: 2. Cosh X y sinh x 2 cosh x sin dx dy dxxy = 1 5. (1-x)

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Q: 1. cos(xy) + secy = 5 2. Arcsin(x/y) = 4x + 3y 3. 4ln(Arctan x) = 1- y 4. y = 5/(sin3x +cos3x) 5.…

A: we have to derivative two times

Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

A:

Q: | (3x – 2x + 1) dx 5. |(x - 1)° dx 6. 7. (x² – x*) dx 8. cos x dx /2 I sec' x dx 9. dx 11. (4 – 2x')…

A: 5. I=∫13(3x2-2x+1)dx =∫133x2dx-∫132xdx+∫13dx =3∫13x2dx-2∫13xdx+∫13dx =3x3313-2x2213+x13…

Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: L{e-4t cosh 2t} L{e=t (3 sinh 2t – 5 cosh 2t)} -

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Q: 4. ox x cost at cost of 3 procuct nule J cost dt + cost at [sint] + x CSLX)ま(x) = Sin x - 0 + x cos…

A: To determine ddx∫0x3 x cos t dt.

Q: The study of undamped oscillations under the influence of an external force F(t) =F0 cos(ωt) leads…

A: Solution:

Q: The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are…

A: The given differential equation is dvdt=-kvn, where k>0 and n are constants and v(0)=v∘. At t=0,…

Q: zln x dx 2) S 3 cos3 x sinó x dx 3) 12.1 dt 13. 3t + 2

A: Explanation of the answer is as follows

Q: Show that (2x cos y + z siny) dx + (xz cos y – x² siny) dy + x siny dz is an exact differential.…

A: Given differential equation,2x cos y z sin y dx + xz cos y -x2 siny dy + x sin y dz =0

Q: A jar contains 100 mL of a certain substance which, when heated to t degrees Celsius contains E(t) =…

A: the given function for the thermal energy is E(t)=2.3t2-4.5 and as the thermometer is accurate to…

Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: Determine the value of ſo1 3.1 X cosx dx by using N= 4 of the trapezoidal rule. Round-off to three…

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Q: (g) y = Vtanh 3r (h) y= sinh(cosh 2.x)

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Q: y = Arctan ( sinh (2x)); y' = * O - 2 coshx /(1+ sinh^2 (2x)) O 2 coshx / (1+ sinh^2 (2x)) O 2/ cosh…

A:

Q: 8) S(eax - e-ax) dx 9) S; sinh x dx 1+cosh x

A: Answer to question number 8 and 9 are as below,

Q: A particles velocity is 7 cos(2t) meters per second. at time t=0 its gone  2meters, where is it  at…

A: The velocity of the function is given as:

Q: ion dy 3t2 dt 2y + 2t3y' tion: ||

A:

Q: 6) S sech (2x - 3) dx 7)S e-e-x e*te-x dx 8) [(eax – e-ax) dx sinh x 9) S 1+coshx dx

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Q: 5) sinh(x)cos(y)dx = cosh(x)sin(y)dy

A: A differential equation (Mdx+Ndy=0) is exact if  dM/dy= dN/dx

Q: Part III - SOLVE the following DIFFERENTIAL EQUATIONS * for partial derivative symbol, use the…

A: The solution is given as

Q: (8 cos x cos y + 4 sin x sin 2y + 1) dx – 8(sin x sin y + cos x cos 2 2y) dy = 0

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Q: 1. S(e2x – 1)3 dx 3. S sin 2x (sin®x + 1) dx 2. S(x6 – 3x²)ª (x5 – x) dx -

A:

Q: (a) f* (1 – cos 3t) sin 3t dt,

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

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Q: Find dy/dt Y=(1+Sin 12t)^-5

A: Given function is y=(1+sin12t)-5

Q: 1. S(esin *cos x – acos 2x sin 2x)dx 2. S(etan x sec x- esecx tanx)sec x dx 3. S dx xvax - 16 3x-2…

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Q: 1. Find given x = 0 - sin 0 dy dx' y = 1- cos 0 1. Find dy given x = et-cos t y = et - sint 3. Find…

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