2. m. n. e G)° dm dn 2 2 m² + m². e(m) + 2n²e)° т

Q: | 21×VX2 + 1 dx = 14 2- 7, what is 21uV u2 + 1 du? Given that %3D

A: The properties of definite integral is ∫abf(x)dx=-∫baf(x)dx. Use the property of definite integral…

Q: Suppose that X, Y C U. If Pr(X) = 0.3, Pr(Y) = 0.32, and Pr(X n Y) = 0.08, what is Pr(X' U Y)?

A: Given :  X , Y ⊆ U . P (X) = 0.3 , P (Y) = 0.32  and P(X∩Y) = 0.08 .  To find : P (X' ∪ Y) = ?   The…

Q: af Find ar ar and ax' ay az 38 Ах, у, 2) x² + yZ + z? af ax ar ay af az

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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: 5. If u = e1#1+az#2++anIn, where a² + a³ + · ·..+ a = 1, show %3D + = U dx?

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Q: %3D 7. If mBC = (9x – 53)' and mCD = (2r + 45)", find mBAD. E

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Q: dt (e2t + 8et + 7)ā et+4 a) 9ezt +8et+7 +C b) In(e2t + 8et + 7) + c 2 c) 5Ve2t+8e*+7 +c e4t d)…

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Q: Solve this egeua tion using differenbicel eque bio us ikx -ik X 4 Cx) s AĈ + 13e

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Q: (b) Show by direct computation that D'Alembert's formula is a solution to the problem U-cUrx 0,…

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Q: 3) u = y f( ise XU, + yu, t zu. = ?

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Q: 10) If 1+ abt = c where a, b, and c are positive, determine the value of t. %3D

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Q: みm 'cU24onba buimoll ut anos Give answers occurate to o tu100yら19 SONe the foilowing tigures 6.8=…

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Q: a²u , a?u k x² ди at ax2 ' ay?, ||

A: In this question, we used the separation of the variable method to solve the 2-D heat flow.

Q: b. y = -In (12yx²) + sin(y)e312xy + e12yx4

A: Given:

Q: : Given a r.v. *=4 3,4,5,then af y= 3x-2, then find ECY), VY) and MCE). Sも), ......

A: Solution

Q: iP fca)ex+s and gixjex?-3- find the folllowiny D Rc fext

A: a)         f(f(x))=f(x+5)           =x+5+5           =x+10

Q: 3) Given: SR IRT; TU LUS; 4STR = 4TSU Prove: A TRS 2 A SUT T R U

A: Given, SR⊥RT,  TU⊥US∆STR≅∆TSU STATEMENTREASONSSR⊥RTgivenTU⊥USgivenSU=TRBoth intercept triangle with…

Q: 5. If z = In , then determine if the following statement is true or false. Justify your answer. a²z…

A: Solve the following

Q: dv/du = (uv)² — 2(u — v) — 2.

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Q: (6) Euter eio_ el" = Cos e +i Sino, whore i = J1. where i= JT,

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Q: o Evaluate , S, Só (x – 2y + 2z)dz dydx.

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Q: After substitution is performed, what is equivalent to u14 du 3 0 9 Su u¹4 du ,14 1. 3u¹4 du 0 2 u¹4…

A:

Q: 7. If (x, y, 2) = 3xz³y – y?, find grad o at the point (1, -2, –1) Ans. - (16î + 9j + 4k)

A: The gradient of a scaler point function φ is obtained by applying the del operator ∇ to the scaler…

Q: too x(Ju) - xt) e ot * the famer heansfarm ナR X( Jw) Sen %3D

A: Fourier transformation of a function x(t) will be X(t) and inverse Fourier transformation of…

Q: 2Iny dy ,2Iny coth e S y csche?y coth e

A:

Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

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Q: E Given: AC= BD D AE = DF ZA = ZD A Prove: ACAE= ABDF F

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Q: If a > 0 and [[ 20*+v 20+u° dr dy = 1(e* – 1) , a =?

A: Using polar coordinate evaluate the above integral

Q: 63. r(и, v) %3D Зи сos vi + Зи sin vj + 18u'k ||

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Q: 3. fualende Zdv, where, E- (nyE):0くn<l,o<y<1-n,oくまく1-1-

A: We have to evaluate the triple integral ∭E z dV where E is the region containing the set of points…

Q: . d the しいwits UI- Vタ+1 ユ ーリー! Cスリ る) しm 5) (Z,y)>(,) Cos Tzyl-a C)にm 反- vy Ca,y)Co)

A: Consider the limits, To solve, Multiply by the conjugate of numerator,

Q: xy In(r+1) rª + 3y? if (x, y) # ( g(x, y) = if (r, y) = ( %3D

A: In this question we will use basic concepts of calculus i.e concepts of limits in two variables. We…

Q: J Ax) dx 11. 12. -3

A: 11) From 0 to 5 there is a trapezium and from 5 to 6 there is a triangle

Q: 2 If [ In(ax)dx = 2, then a %3D 1 e4 4 None es 4 4 4

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Q: a. m arc AB = 80°, m∠AEB = 75°, m arc CD = ? b. m arc AC = 62°, m∠DEB = 45°, m arc BD = ? c. m arc…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: B 2. 7.2.Preve that CD= 24 SnR Vzt2 cosx

A: Use trigonometric ratio to solve

Q: 28t(7ピー5), ScI) =2 %D soloution=?

A: Given,           dsdt=28t7t2-53 and s1=2

Q: 31 (C) (: (0)/ (zcos () dz

A: Here we will do integration by parts to find the value

Q: 4. Evaluat the fellowing using Simpson's ţ ruloi h =d *x?dx;Ans.c(8.667) B-SとJx iAns. (8、み59)。 A-」

A: By using Simpson's 1/3 rd we have to find solution of given integrals.

Q: What is the value of w,(r, 0) at r= 1/2, 0 = 1/2 in Question 7? 1+ 2 et 4 4

A: We have to solve the problem

Q: F(u,v)=(uv)e, +(2uv)e, a) Is conservative?

A: For calculating the vector is conservative or not. We will have to find out curl of the given vector…

Q: In 2 (In 2)2-y2 evx2+y² dxdy 0.

A:

Q: 2- Evaluite the Value of 4he next nteg Pation by using Ahe trapezodal rule ; Then Find the absoluto…

A: Given the integral                                   The trapezoid formula is given by where…

Q: Find u(x, t) which solves the problem Utt = 9urr -00 < x < o0, - 0 <t <3; 1 u(x, 0) = 1+ x2 Ut(x, 0)…

A: D'Alembert Solution;    u(x,t)=ux,t=12f(x+ct)+f(x-ct)+12c∫x-ctx+ctg(ξ)dξ where u(x,0)=f(x),…

Q: Suppose that X, Y C U. If Pr(X) = 0.4, Pr(Y) = 0.22, and Pr(XnY) = 0.07, what is Pr(X' U Y)? %3D

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Q: Show that if Y = ax+ b (a ≠ O),then Corr(X, Y) =+1or -1. Under what conditions will p =+1?

A: Assume that X has has nonzero variance, since otherwise the correlation coefficient would be 0,…

Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3

Q: 16 Find Ehe eract length of Ene eurve, /2 x= e- 4E, y= Re O<6< 2

A:

Q: a) b) Compute E(X|y), Var(X) and Var(Y). Hence, deduce the value of p= Corr(X,Y).

A:

Q: OC {(z, 9) 2? + y? z and z € (-1,1]}- O D. {(x, y) + y? z}-

A: We have to check

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.