GIVEN: TV || WY with transversal RS W. MZRUV = (r + 4)(x – 3) R mZWXS = x? 3 3/X FIND: 2.

Q: Find r'(t).

A: We have to find r't: rt=4ti+t2tj+lnt2k We know that dxndx=nxn-1d lnxdx=1xd lnfxdx=1fxd fxdxdxdx=12x…

Q: А- If v = t". et. Find the value of n, which satisfies the equation ar (r2 = r2 dv at

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Q: 6 If x=25eco, y=4tan8. Evaluate dy where B= Lrad Ans/-0.2647

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Q: dy Find for the following by using appropriate rules: iv. x² + y3 + (lnx)e♥ = 4. y = Vx(3x2 – 1) V.

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Q: Evaluate ſſs 3y dS where S is the portion of y^2 + z^2 = 4 between x = 3 and x = 3 - z. %3D

A: The surface is ∬S 3y dS=∬S1 3y dS+∬S2 3y dS + ∬S3 3y dS

Q: If f(x,y,z) = e2x+3y-4z + xyz And x = 3si n(rt) y = 2cos(rt) z = r² + t² af Find at

A: Given that,  fx,y,z=e2x+3y-4z+xyz And  x=3sinrty=2cosrtz=r2+t2 If F=fx,y,z, Where, x, y, z are…

Q: Hawis Find d Vand V2if vI+2V2=31-k and 3V-V2 si+j+k

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Q: Use the trapezoidal rule to find AT using the indicated value of n. 8 dx; n = 8 2x2 +2

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Q: dy Use separation of variables to find the general solution to dr + 4xy? = 0. %3D

A: We have to sine given differential equation using seperation of variables

Q: If f(x,y)=xe/2,+37x?y3, then dx²əy³ at (1,1) is equal to

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Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: et f(r, y) (-(4r + y)) Then %3D ardy

A: The given differential equation is: f(x,y)=-(4x+y)7

Q: If a particle is moving with v(x)=1.5(x^1/2) and s(9)=33, what is the position of the particle? As a…

A: Let v(x) denote the velocity of the particle and s(x) denote the position of the particle.Obtain the…

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: dy Find at (x, y) = (3, 4) and z? = a²+y² if d = x² + y? if 1 аnd 2 6. dt

A: Given z2=x2+y2, (x, y)=(3, 4), dxdt=1, dydt=2. When x=3, y=4, z2=32+42   =9+16   =25 ⇒z=5

Q: For x=e2 y= In 2t, find the value of k so that ky'=1 at x=e

A: Given: x=e2ty=ln 2t

Q: 3. Find.the..velocity..Specd.and.aceleratem.for the followmin.positiom.vecetorsis .. .. *ウ… t=..32.…

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Q: In Exercise, verify that S and T are inverses.

A: GivenS:R2→R2 by Sxy=4x+y3x+yT:R2→R2 by Txy=x-y-3x+4yTo check S  and T are inverse of each other.

Q: ン Frnd in side r=2 inford quarler aren aul sde r= 1+s6

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Q: Given f(x,y) = ex cos y, Evaluate fx(2,0)

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Q: If f(x, y) = 8xey + 8y Inx, then is given by:

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Q: 2. If LM = 10 and PS = 11, what is KN? ls 3. If PS = 2x + 4 and KN = 5x+ 2, and LM =-3x + 8, what is…

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Q: Wi- Find the where (221) م 270 ل 24 4 2 0 :C للنووزه value of - COSTI Z dz

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Q: The mgf. of a r.v. X is (}+3) (+e) . Show that 9-x Ρ(μ- 2σ<X<με 20 - Σ (!) ( (3) P (μ- 2σ< <μ+…

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Q: Suppose that f(0.25) = f(0.75) = B. If the Composite Trapezoidal rule with n 2 gives the value 4 for…

A: The formula for Composite Trapezoidal rule is given by, ∫abf(x)dx=h2f(a)+2∑i=1n-1fxi+fb where…

Q: dy 5t vi (In(t) + 1) Vi dt

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Q: Aet statyested that PON fghle v wi the nest presintenS 0 v e rand ptaton of a e voen probatity tha…

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Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

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Q: Q3. Find af and at se If f (x, y) = 2e* + Iny2 ,and x = 2t + r2, y = ar r+1

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Q: onti at t=2 & cx) = 6 r X <2 メー 3メ+2 /25メ<3 is fis wnti at

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Q: Use the Midpoint Rule with m = n 2 to estimate the value for 5 x + 3ydA on the rectangle R = (0, 8]…

A: Given fx,y=5x+3y

Q: f[x'+zy2,y²2x2], then prove that [y?-zx] (a?-yz] dy [z-xy] du -o. If

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Q: - show that; L-1[e¬v$] = e %3D 2tynt

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Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: 2. For what value(s) of h, y belongs to Span {v1, v2, v3}? Where 5 -3 V2 = -4 V3 ,and y = 3 h

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Q: To F= G(s)= B(s) 2555+35 + 6 %3D A(S) stos't l1lS+ 6 Find F4) b] laPlase?

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Q: %3D 23. f(x, y, z) = 2x + z? subject to x² + y? + 2z? = 25

A: Lagrange's Multipliers: The Lagrange method is used to maximize or minimize a general function…

Q: If f'cx)= gica) for 0LKLH, then fca)=9(x) for OLxel True or false?

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Q: Given f(x, y, z) = In(x² + y? + z?), show that 2 dy? d22 x2 + y2 + 22

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Q: Find f f'Lx) = ZR? +aX-S and %3D to FlO)=4.

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Q: af when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y ,x = 2t + s, y = 2s – t. a) Find as

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Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy – 4y. Then:

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Q: Use the False Position method to find an approximation to the value of v7 that is accurate up to…

A: False position method formula x2=x0-f(x0)⋅ x1-x0 f(x1)-f(x0)

Q: Given: f (x, y, z) = 2x'yz² + 5x°y*z® - x³y? ,5_3 Required: fzyx , fxzz

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Q: Given f(r, y, z) = v 4x2 + 6y² + 3z?, find

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Q: f(z) =z? is discontinuous

A: f(z)= z2 is a polynomial function in z and polynomials are continuous everywhere.