8 + x –1' 2(x– 1) Which of the following expressions is equivalent to the one above, where x + 1 ? 9. A) х — 1 | 14 B) х — 1 15 C) 2х - 2 21 D) 2х - 2

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: 5. Determine given: axty - bxy = 36 %3D where a and b are constants.

A:

Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: 4.3 Use the calculus of residues to evaluate the following integral 27 1 do. 1+8 cos? 0

A: Note:-  cosθ=eiθ-e-iθ2 Residue Theorem:- ∫Dfz dz =2πi ∑k Res fzk=2πi×sum of residues   Given that…

Q: 2 sinºe cos³e de= 60 a O 120 b O 1 .c O 60 .d O 120

A: We have to solve given problem:

Q: 8. Solve the following IBVP: U = u + sin(3nr), 00, u(0, t) = u(1, t) = 0, t20, u(r,0) = sin(72),…

A: Given ut=uxx+sin(3πx), 0<x<1, t>0u(0,t)=u(1,t)=0, t≥0,u(x,0)=sin(πx), 0≤x≤1

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

A:

Q: Let o,= 2 (cos 45° + i sin 45°), @,= (cos 30° + i sin 30°), calculate a. @j @2= b. o, / 0,= с. О d.…

A:

Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

A:

Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

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

Q: Let p and q be integers with q > 0. If y = x, differentiate the equivalent equation y = x°…

A:

Q: Use Euler's method to obtain a four-decimal following: approximation for t (4 y=2Xy, yC)=1; yU5) =?…

A:

Q: * S[*****] = Yg = 1 + +x² + %3D + de 1 + x* + 24 3 1 + 24 3 오4 4 +x2 +x + T 24 3 4 24

A:

Q: Find U from the differential equation and initial condition. I'm know the answer but I don't know…

A: To solve below initial value problem.

Q: (r(1/4)|? 4u/27 dv Prove that

A:

Q: 6. If f(x, y, z) = r³y³ sin (z²)+z³ cos (r³), find an expression for fryz and evaluate it at the…

A: x, y and z are the variables of function f Differentiating partially the function f with respect a…

Q: Evaluate 1. (5x + Vy) ds where C is given in the accompanying figure. (1,1) 1- y =X y=x? (0,0) J.(5x…

A: Solve

Q: 1 1 dr = In a. find the exact value of a. %3D V16+9x? 19+4x*

A: Here we will solve for 'a' step by step answer given below,

Q: 3. Show that the following ODE is homogeneous then solve it. 2xyy' = x2 + y?

A: 3). Given: 2xyy'=x2+y2 So, we can also write as: 2xydydx=x2+y2dydx=x2+y22xy....1 Let,…

Q: The approximation to a root of the equation x^2+x-1=0 in the interval [0,1] b applying the regula…

A: The given equation is x2+x-1=0  find the value of f(0) and f(1)  fx=x2+x-1f0=02+0-1=-1…

Q: Prove L{a coskt}= -at S+a

A:

Q: By using Residue fined S 2+3 sin z(z-1)² dz, C:|2|=2? (6 €13) (4

A: See the details solution in below

Q: What's the value of the integral (2 - 1) dz from (1+i) to (2+2i) a. 17 + 11i b. (11 + 10i) /3 C.…

A: The solution is given as

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

A:

Q: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate w when…

A:

Q: Given: mzQVR = 49° Prove: x = 15 R V (3x + 4)° U Complete the steps of the proof.

A: Given ∠QVR =49°    and ∠TVu =3x×4    We know ∠QVR =∠TVu             ( as both are vertically…

Q: 1. true or false. justify your answer. (a) |x+iy| ≤ |x| + |y| (b) arg(-2+10i) = π – tan−¹(5) + 2nπ…

A: Given statements,  (a) |x+iy|≤|x|+|y|  (b) arg(-2+10i)=π-tan-1(5)+2nπ for n an integer. The…

Q: all Metro by T-Mobile ? 5:56 PM @ 25% - Use Pythagorean theorem to find ri... 16 12 Choose 1 answer:…

A: Using pythogereon theorem

Q: T/2 TT/6 sin x 2 1.)Prove that

A:

Q: 11T 60. Given that sec 12 13T V2 - V6, determine the value of sec 12

A:

Q: 2ху 3. y' = -x?

A:

Q: Q: Prove that : sin' ne -de = na for all n e N. sin' e

A: solution is given below

Q: •1-i Evaluate 4z dz . J3i

A:

Q: U Sin/X-Y Show that Itanu. 2. LL

A:

Q: Verify by direct substitution that Un(x,y)=sinnx sinhny is a solution of Uxx+Uyy=0 for every n>0.

A:

Q: 3. Consider tw o evénts A and B such that Pr(A)= 1/3 and Pr(B)= 1,2. Determine the value of Pr(B 0A)…

A: Given PrA=13 and PrB=12 and A and B are disjoint, that means PrA∩B=PrA×PrB…

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: In order to evaluate Vx2 - 6x + 45 d, the correct substitution is Ox = 6 – 3 tan(t) O x = 6 + 3…

A:

Q: Which of the following is true? 1 dæ = In 2x +1+C 2x +1 1 D In(2x - 5) %3D 2x 5 | リ+ 1)? 1 de = In…

A: The given options are (i) ∫12x+1 dx=ln2x+1+C (ii) Dxln2x-5=12x-5 (iii) ∫1x+12 dx=lnx+12 +C (iv)…

Q: 1/2 cos t Evaluate the integral o dt. 4.- sin? t In a Give your answer in the form where a and b are…

A: Given: ∫0π2cost4-sin2tdt Let sint=xcost=dx Then sin0=0sinπ2=1 So, ∫0π2cost4-sin2tdt=∫01dx4-x2

Q: 59 AM Thu Mar 4 * 69% + : 0 12. Find all solutions of the following equation on the interval [0,27).…

A:

Q: Show that the DE is exact, then solve it. 2.a²y' + 4.xy = 3 sin x, y(27) = 0

A: Let us consider first order differential equation dydx+P(x)y=Q(x) The differential equation is…

Q: 1 Using the fact that 1 du = -tan (-) +C, which of the following is equal to a² + u? 2x dx? o 16+x

A:

Q: 4.3 Use the calculus of residues to evaluate the following integral 2m 1 de. 1+8 cos? 0

A: We find the given integral by using calculus of residue.

Q: for a>0 is defined a n(x² + a²) and sin ax = (x)"6 prove that la * fb = fa+b and ga * 8b =gmin (a,b)

A:

Q: Which of the following is Inx – 6x + 18| + arctan(- (x – 3)) +C equal to? 2 – 6x + 18 x - 3 V 2 In…

A:

Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

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: (a) Let m and n be positive integers. Show that T if m = n, sin mæ sin næ dx 0 if m + n.

A: We know  Sin^2x= (1-cos2x)/2

Q: If r(t) = (VE – 1, ln(10 – t), sin(2t)) then the domain of r is

A: