X sec10 can 1. Let u = 7 In х2 - 1

Q: [ 1 If A= -1 0 find x and y such that (xI +yA) = A

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Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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Q: 2. Show that c(x, t) = solves 1 ac(x, t) 2 ax ac(x, 1) ar

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Q: The convolution of e2t ® sin(3t) S is | e2Usin(3t – 3u)du e2usin(3t – 3u)du Se-2usin(30)du…

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Q: Give the condition which ensure that Je-| < 1 where z E C.

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Q: y If z = show that = 0. x + y?*

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Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

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Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: xy If z show that: x- y

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Q: 3. Solve the following IBVP: Ut = Uzz + sin(37x), 00, u(0, t) = u(1, t) = 0, t> 0, u(x, 0) =…

A: Solution

Q: ze : use the Implicit Differentition to find ax 'ay 1) 3yz2 - e4* cos 4z - 3y2 = 4

A: 3yz2-e4xcos4z-3y2=4

Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: Prove that: sec a + sec(120° +a)sec(120° – a) = –3 sec 3a

A: To prove that  secα+sec(120∘+α)sec(120∘-α)=-3sec3α

Q: Solve the following aw dw aw. Q1) w(x,y, z) = xy²z³ + esin(x*y²z) + x² – y³ + z – 7 find ( дх ду az

A: Here x,y and z are independent variables and w is the dependent variable that depends on x,y and z

Q: 3 of u(a,9) = Cof"( 4y Cof' (+y then provethat ace +4u + Sin2ce=0

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Q: O cos Z 12 15

A: Right angle triangle

Q: Prove that d (sec"x)= 1.

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Q: Hence, using chain rules find y' i. y = sin(2x² + tan(6x² – x)),hint: u = 2x² + tan(6x² – x) ii.y =…

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Q: (6) If u, =*-!P«(x)Pn -1(x) dx, show that nu, + (n – 1)n-1 = 2, %3D and hence evaluate u„.

A: Given un=∫-11x-1PnxPn-1xdx

Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: az Find if yz – In z = x + y ax 3.

A: We have              yz-lnZ=x+y

Q: s show that: sinhCA+B) = SinhA. cush B + Cosh A. simhB

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Q: 2) Show that La- (1 – x²)P',(x)P'm(x) dx : 21(1 + 1) Sim. 21 +1

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Q: 2πί -dz = 9. CoS z Iz=2 z3 + 9z :Select one True False

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Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: al HL b7 SAS C) NOt Co ng ruent

A: We will prove what relationship these two triangles have.

Q: The energy stored 'W' in an inductor is given by W (10 * 10-3)te-2dt %3D

A: Given query is to find the value of the integral.

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

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: •1-i Evaluate 4z dz . J3i

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Q: 25 -x2 -dx, if we let u=/25 – x? , then udu =- xdx. In A) True B) False

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Q: d 1 - (sec-!r) = dx Prove that xVx - 1

A: Let y=sec-1xsec y =xcos y =1x.....1 Thus sin y=1-cos2y=1-1x2=x2-1x2=x2-1x .......2

Q: 10. f(x) =-x2 +3x+ m, y 4-IOBI = 10CI %3D A(ABC) = ? B.

A: As per guidelines, we will solve first question poste. 10) Given fx=-x2+3x+m 4OB=OC

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: 2 7 4 is S cos' xsin xdx 비

A: See the details solution in below

Q: F Sin(ncso)- Cscrsin o) , thes the valke of 10+4).

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Q: If Cov(x,y) = 0, then X and Y are uncorrelated Select one: O True False

A: If two variables are independent then their covariance is zero and we, say that they are…

Q: ion Prove that for

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Q: 2. Solve: tan(3 T - 4) = 1 Te [0, 1 %3D 2 T = 80 %3D 10 3 A %3D 25 T = 20 %3D 3 л

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Q: If f(x) = 12sin(green wave), then the red wave isi %3D 20 |-3T/2 -TT T/2 TT 3h/2 2n |-10 IF f(X)=12…

A: Red wave satisfies the point -π2,0,3π2,0  a) Given,   6sinx+π+6 Put x=-π2…

Q: 11T |13T V2 - V6, determine the value of sec 60. Given that sec 12 %3D 12

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Q: Find an expression of for y = 2*ev*, Hint: (a*) = a* . (x) · In a

A: We can find the derivative as below

Q: vsin ax (02+4)4= sin x is the fun ction with y %3D

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Q: Let A + 0 and ACB. Show that NB CNA.

A: Given :A≠∅A ⊆ B