2 Evaluate: :S,vte-t² dt.

Q: rsin z Find dr V2+t+t) dt.

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Q: 3. RT = 22 and US = 18 VT = UV = S RS = %3D U T.

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Q: a2 If a;j = aji (ajX;X;) əxyəx; are constant, calculate %3D

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Q: If u = a + j13 and v = -11 – jb, calculate Im(u + v).

A: Add the two complex numbers then write the imaginary part.

Q: Lw(s) ~ 1 – Show that 1 is MTTF where

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Q: Use the substitution formula to evaluate the integral. 2t dt -1 18 36

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Q: 2. What is the relation between dV /dt and dr/dt if V = ()7r? %3D

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Q: Q3: show that: S yi va -y dy =na² where a is a positive constatnt

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Q: jn= 16, α=0.05

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Q: Q3 Evaluate fII, xyz dxdydz, 3 < x < -2,0 < y < 1,0 < z S.

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Q: The DE : y' = e5x-7y is seperable Select one: True False

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Q: mTQ = %3D mQR = %3D U 44 mTS %3D T. R 25 MSQR %3D MRQT %3D

A: Problem 1   Problem 2

Q: EX: Verify that z= I+ V3i satis fies the 2. eq.

A: the given equation is z2-z+1=0 given the value of z is z=1+3i2 substitute the value of z in the…

Q: - (a x r) = a x r' for any constant vector a. dt Show that

A: To prove: ddt(a×r)=a×r'. Consider L.H.S. Differentiate with respect to t using product rule.…

Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

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Q: nto v. t of u orthogonal to v.

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Q: What is the antiderivative of J (5t° 2t* + t + 3) dt. c.t° -+t + 3t 2 а. t5 +t2 + 3 с. b. t° -t5 +t2…

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Q: rsin z O Find V2 +t+t2) dt.

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Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: 2 calculate J= e dyok 2x

A: Given integral :

Q: Find v(t) from tre Sepvabe equanon: dv = 9.81-느v 1. (981 -KV) 100 9.81-Ev = %3D 100 dv 1 (981-KV)…

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Q: im(z,v) →(0,0) F(x, y).

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Q: The DE : y' =e3x-7Y is seperable Select one: O True False

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Q: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

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Q: 3. Vsech 2t Evaluate dt 3. coth 2t

A: Application of integration

Q: 2. Evaluateſff, y dV, where: E = {(x,y,z)|0 <x< 1,0 < y < 4x,y < z < x² + y} %3D

A: The solution are next step

Q: 8. Show that jxk i.jxk (а) і— kxi (b) j= i.jxk ixj (c) k =- i.jxk

A: Topic = Vector

Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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Q: Evaluate Sm e" dæ. • 2 does not exist (diverges)

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Q: Q2:show that the force Fexyzi-x4z'k is Conservative. ?

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Q: In the integration of (csc 5t)(cot 5t) dt, what is the correct "u"? O (csc 5t)(cot 5t) O csc 5t O…

A: I=∫csc5tcot5t dt Let 5t=u ⇒d(5t)=du⇒5 dt=du⇒dt=du5

Q: J sec° (10t) tan“ (10r) dt 4 10.

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Q: t dt 212 + 8

A: First calculate the integral then apply the limits

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: et + 6e3t + 12e2t +9e dt. (d) Evaluate the integral / (e2t +4et +5)2

A: First, simplify the integral. As the degree of the numerator is greater than the denominator, use…

Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

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Q: Je find The general Solutivn od DiE+

A: The detailed solution is as follows below:

Q: R Given: RS UV RT RS Prove: VT VỤ

A: We are given the two triangles as :…

Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: b) u(х, у) on the domain 0 < [z| < ∞. x² + y? Why is v(x, y) single-valued in b?

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Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: Consider Y; = 0 + 0,X¡ + E¿, i = 1,2,..,n, e, - N(0,0), the cov(ô,Y) = %3D

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Q: V- Assuming Cov(X, u) = 0 allows us to equate Ex û to zero. True or False? Explain.

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Q: (b) Compute f er+uds, where c(t) = (t, 2t), t e [1, 2]. %3D

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Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.

Q: Evculucte the ntegre ree)dt where re =secttleH, tine TNt C 2

A: The given function is

Q: Evaluate z cosz dz where C is (1)|z – 1| = 1 (i)피 = 2

A: Answer

Q: Solve the folleowing differntial equations by usina Lapace trans formation dy dt +243D 1 + 2 dt2…

A: Given Differential equation :

Q: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?