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Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

Q: 3). wh.ch of these condition ally Ca uvergent! Tuere may be more than 1 right answer. Odre arctan u…

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Q: /2 1lf If In = " x cos" x dx, when n> 1, show that п(п — 1)1-2 — 1 In 12 [Hint: cos" x = cos²…

A: Given: In=∫0π2x cosnx dx

Q: S =m sin(3x)cos(5x)sin(7x) dx: (sin(5x)sin(9x) +sin(x)- 15 sin(15x) +C (लड 4 Select one: True False

A: Let's find.

Q: Compute for the value of tanh (1 – i) Iny + 2.13i In 2 + 2.13i 2 In 5 - 4.25i 2 In v2 + 2.13i

A: To Compute: tanh-11-i Concept: 1. tanh-1z=12ln1+z-ln1-z2. lnz=lnr+iθ+2nπwhere,…

Q: show that Itu X tvl = Oe sinu far a sphene of a radus a depined Panamet ui call y by 9 cU,V) =a…

A: Given: Parametric form of a sphere with radius a…

Q: If I, = S e cos" xdx, where n > 2, prove that In 1+n(n-1)In-2 n² +1

A:

Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

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Q: 11. An expression that is equivalent to 2tan z Otan z Ocot z 02 cot z sin 2x 1-cos 2z is

A:

Q: (종-272 27=) + ain G + 272) The simplified form of cos O V3 cos 27z + sin 27z V3 cos 27z + v2 sin 27z…

A: Given cosπ6-27x+sin(π3+27x)

Q: If r = (3 cosh 2t)i + (3 sinh 2t)j + 6tk and t = In 2 then اخترأحد الخيارات 8. 16 and T= 867 O K =…

A: Curvature   k=32867=0.0369088811995386.

Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

A:

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: (/2 x cos" x dx, when n> 1, show that Jo If In п(п - 1)1,-2 — 1 In [Hint: cos" x= cos? x.cos"-2 x…

A:

Q: Use the properties of logarithms to write the expressions in Exercises 43 and 44 as a single term.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: O if Z= x'tan!Y final dž Handwriting Point Cl,!) In

A:

Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

A:

Q: 1²–1 True or False: cosh (sinh (In æ)) = Select one: O True O False

A: Given: cosh(sinh(lnx))=x2-12x. The objective is to verify the left hand side expression.

Q: 3 Evaluate the gwen tri ple in legral. xsiny dy dz dx

A: Order of triple integral dydzdx

Q: 4. p² –1) cos[cosh (In r)]dr let u= du=

A:

Q: 43. If |2| > 2, then f - dr r = fcos(5) + k B sin-'(5) + k: cosh-" (5) + k: Itanh-"(4)+k B 2

A: by using hyperbolic Trigonometry substitution

Q: dq + q = 4 cos 2t dt

A: Given that, dqdt+q=4cos2t On comparing with general equation dydx+Py=Q ⇒P=1, Q=4cos2t, dx=dt…

Q: 1/w cos Tº If h(w) = 10 -dz then h'(w) = (m),4

A: Given:-h(w)=∫101wcosx9x2dxTo find: h'(w)

Q: 2 If s Sinants COs ant 3 an= ০ । A. limitdoes not exist 2.

A: Series and sequences

Q: You hare shown that e jul dw or , erchenying w and t Jlw) = Use a chume of veriables to genenle…

A: Consider the given information: δ(t)=12π∫-ωωejωtdω                  ..(1) δ(ω)=12π∫-ωωejωtdt…

Q: Prove thet (1+ cose -isine)" +(l+ Cos e+isine)" = 2""cos (em). %3D Co."(을) COS

A:

Q: 1. Find fr fy and fry if f(x,y) = y* + x?y + In xy.

A:

Q: Nhat is Duf at P(1, 1) if f(x, y) = sin(x - y) and u=i-İ? 3 O 5 O 3 4 O 10 9

A:

Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x>0 we have to prove that…

Q: S-) Find the gereral solufon of Sin'x y"- (2sinx.cos x)g'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Given differential equation is sin2xy"-2sinxcosxy'+cos2x+1y=sin3x Here, qx=sin3x Given that y1=sinx…

Q: to to TD)=e sint i te cosi cosy %23 ek Hongehtia componen't 5 of acceler Find the and hormal any…

A:

Q: 1. Ir Y= 4 In (In (In(sec(x)) then Y =[4 (tan)/{ In ((In (sec)) In (sex)}] O True O False

A: Y=4lnlnlnsecx remember chain rule ddxlnfx=1f(x)ddxf(x)

Q: 6. Which of the followg quti dy (a) de dy (b) de () +2ry- (e) (4) Al of the above

A: It is given that There are four differential equations option.

Q: 4. Show that In sin 6 d0 = – n 2 by applying the mean-value principle to In |1+ z| for |2| <r < 1,…

A: ∫0π2logsin(θ)dθ=12∫0πlogsinθdθ                         =12∫0π2logsin2θdθ…

Q: 5 Evaluate ſ“ S" r² sin ø drdøde 0,

A: Evaluate: ∫02π∫0π∫05r2sinϕdrdϕdθ

Q: S(32+2*)sin(z)dz 3z +

A: In this question we have to solve Integration.

Q: Given that L tsinh 4t]= 8s , use the First Shifting Theorem to compute (s -16)? L [te 4t sin h 4t1…

A:

Q: 3 Prove Prive that d tin'u e I du

A: As we now the identity tan2(x) +1=sec2(x)

Q: + 8z7 – 5 sin z)dz O 4e -z +5cos z +e O 4e +z" +5sin z +e O 4e +z* - 5sin z +e O 4e +z – 5 cos z +e…

A:

Q: (osh x- Sinn? 21 Sin nx=1 20 (Osh K= ?

A:

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

A: x = sect y = tant

Q: in a paragraph proof please

A:

Q: 8 21. et dt 7t sin(9x)

A: ∫sin9x8et/7tdt

Q: 2)If X is exponentiol with porameter A ond Y is expom with parame ter B, ond X &Y are inde pent,find…

A: