lim Y+ Y Cos y Yo 4 Siny cosy

Q: 1. cosh z= cosh x cos y + i sinh sin y sinh z = sinh x cos y + i cosh x sin y.

A: According to our guidelines we are supposed to answer only one question, since you have asked more…

Q: 11. I+ tancay)-o 12. + siny-x'y

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Q: sin (x + y) %3D coS Xcos y 7. tan x + tany

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Q: QI Evaluate 2 2 || 2y2 sin(xy) dydx 0 x

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Q: いpO O siniz iff Z-kTi,K-o,っ3リーー Sin iz ニ

A: we have to prove that siniz=siniz¯ if and only if z=kπi, k∈ℤ.

Q: y Lim 2+sin y y-00 y2+cos y

A: We have to find: limy→∞y2+sin yy2+cos y We know that sine and cosine function are always vary…

Q: sinh (iz) = i sinz sintiz) =isinh z,escia)= cosh: 2. !!

A: In this question, the concept of a trigonometric function is applied, Trigonometric Function The…

Q: dy - x = x2 siny dx 3 -2 =-(-siny +cosy + Ce-y/?)*? ANSWER: x = + cosy + Ce

A: We will find out the required solution. Kindly note that there is misprints in question which has…

Q: squa roots mplex humber 5 + 21. (cos 0+j sin 0)® (sin 0+j cos 0)* 2. Express in the form x + yi.…

A: We have to find the x+iy from.

Q: sin 3y cot 5y Q7// Evaluate limy-0 y cot 4y

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Q: tan x + i tanh y 1- i tan x tanh y 18. tan z = tan(x + iy)

A: We have to prove

Q: (Integral sign) t cos^5 (t^2) dt

A: Integrate by substitution

Q: Cos (x-y) t cos (Xty). COS 2cos x COSY

A: (Cos(x-y) + cos(x+y)) /2.cosx.cosy =?  We know that cos(x-y) = cosx.cosy+sinx.siny…

Q: sin 3y cot 5y Q7// Evaluate limy→o° y cot 4y

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Q: sin(x + y) - sin(x- y) 2 cos x sin y

A: Solve the following

Q: eiz-e-iz 1. Show that Sin z 2i

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Q: lomain of y= sin3x i

A: The graph of sin 3x is continuous on the entire number line.

Q: tan y-1 . sin y- cos y- 1 www. Prove that tan y +1 sin y + cos y+1 2.

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Q: integral Scos 4 (3x) Sin (3x) dx Evaluate the

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Q: sinh (u+v)=sinhycoshr+ coshuxsinhv

A: Use hyperbolic function

Q: Find the limit

A: We write the expression using sin and cos

Q: y = tan In(x + sin x) %3D y = sin x + In sin e* %3D

A: y=tan ln(x+sinx) y=sinx+ln sinex

Q: sin³ y dy 2. S 1- siny

A: Solution Given   ∫sin3y1-sinydywe need to find the integral

Q: sin 3y cot 5y lim y→0 y cot 4y у cot

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Q: y = Vr² + VT etin e y = r-5 y = (cos z)n. y = /tan 2x – sec3 (4x – 1)

A: as we are just given 4 functions and not any question so I assume we need to find the derivative of…

Q: Hiw/ It isinh z = Siniz, prove That: sinhz = sinhxcosy tising cosh x

A: Given - If i sinhz = siniz To Prove - Prove that sinhz = sinhx cosy + i siny coshx         Formula…

Q: ation (1+xcos 2y)dr-x'sin 2 ydy = 0. %3D

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Q: Find the limits

A: Consider the provided expression, limx,y→0,4xy Find the limit of the provided expression.

Q: (sec2 0 – sin 0) de sec y (tan y – sec y) dy 1 2

A: Given:- 1. ∫(sec2θ - sinθ)dθ2. ∫secy(tany-secy)dy

Q: cos x- cos y X, =0, y,=0; sin |x|-sin | y | x, 0, yo=0; B) f (x, y)= %3D %3D r) f (x, y) = %3D %3D…

A: As per bartleby guidelines, for more than one question asked, only one is to be answered. Kindly…

Q: salvepE tany= Sin(2 +y) +Sin(x-y) (ans. secy= C-2 Casx)

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Q: sin 3y cot 5y Evaluate limy-0 y cot 4y

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Q: Cycloid arch: x = a(0 – sin 0), y = a(1 cos 0) - -

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Q: Find the limit

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Q: Cos ly -A) %3D show that 2 ニ0 2 8x Sx8y

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Q: Ci-2)x OS how that dx = where cis constant of integratron abore or Otherwise Using find f ansurer -2…

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Q: ysiny limy-»o (y+siny)²

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Q: i. y = sinh-1 (x), ii.y = cosh-1 (x),x > 1 iii.y = tanh-1 (x), |x| < 1 %3D

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Q: Prove Jhab sinY Tim lim e-1 lim Sin y ニ ン と Siny S iny

A: Given,            limx→0sinxex-1=limx→0ex-1sinx=limx→0esinx-1xTo find : Prove the given limits.

Q: (xSin 受)x x cas dy -y Cos X Cos

A: Thr solution is given in the next step.

Q: e) cos (x + y) - cos(x - y) =-2sinxsiny

A: The LHS of the given equation is cosx+y-cosx-y. Note that, cosA+B=cosAcosB-sinAsinB and…

Q: (1+siny)[1+sin(-y)]=cos2y

A: Given:

Q: sin (z. + za) g.= = [cos (z, – z)] (/Zn + z,) + z.) h.== tan i. 2= csc (za - za)

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Q: y' + y" = siny O 1st order, 4th degree 2nd order, 1st degree O 4th order, 4th degree O None of the…

A: Given problem :- y''+y''''=siny  To find:-  order and degree of given differential equation

Q: lim y→0 sin3y/4y

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Q: Hei! If y cos(xy) dydx = x=0 y=0

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Q: 9. lim -cosy y>0 sin? y sin y 10. lim y»z 1+cosy sin ax 12. lim x→0 sin bx 11. lim x csc 3 x

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: lim sin(2z) = z-/3 %3D /3 2. 1/2

A: We need to find limx→π3sin2x