3 (5) Suppose that T : R³ → R² „such that 2 1 1 T (e,) = T(e.) T(e,) = and T (e,) = 1 1 3 2 T Find - 1 3.

Q: 4. Solve the equation T _ ²T dt ax satisfying the conditions: (i) T=0 when x= 0 and 1 for all t 2х,…

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Q: Then, the only positive equilibrium point of Eq.(1.1) is given by (2.7) (1 – A) (E Bi) Li=1 provided…

A: Given linearized equation of Eq(1.1) about y~ takes the form ;…

Q: Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row…

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Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

A: What is minimum and maximum Value: For a given set of numbers, the minimum value of the set is the…

Q: EXAMPLE 2: dz 1 Given that z = x+y,where x = and y 2r. Find by: dt 1 a. Substituting x= and y = 2r'…

A: From the given problem:   z=x2+y2 ; x=1t2 ; y=2t3 a). Now, substitute x=1t2 ; y=2t3 in z=x2+y2 .…

Q: Exercise 3: Suppose that in an electric display sign there are three light bulbs in the first row…

A: As student want answer of only part 3,  So, I am providing the answer for that part only.

Q: (1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0)…

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Q: 4. Solve the equation satisfying the conditions: dt ax (i) T=0 when x= 0 and 1 for all t 2х, 0Sx<1/2…

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Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: Prove 8xyz < (x + y)(y + z)(x + z) for every x, y, z E [0, +∞[.

A: We have to prove given identity: Concept:

Q: Cons i der the linearsystem X2 1. 2. is Gauss-s eidel method

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Q: .Prove that e- -dt < (1+ t²)* 1/4 6.

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Q: Find the Tians Farm F(s) = "suy (27>1>0) (1 – s)(1 – e **) 3) f(1) = e',

A: Given problem:- Find laplace transformation of f(t) =et (0&lt;t&lt;2π)

Q: -2+z) ds over t e point (0, 0, 0)

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Q: 2. Show that if zo is an isolated singularity of f(z) that is not remov- able, then zo is an…

A: We have to show if z0 is an isolated singularity of f(z) that is not removable, then z0 is an…

Q: 4.) Suppose X has moment generating function MX(t) = 0.3e−t + 0.1 + 0.1et + 0.2e2t + 0.3e3t. What is…

A: It is an important part of statistics. It is widely used.

Q: 2. Show that 4=x i+y°j+:'k is irotational.

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Q: For or x=t- In t y=t+In t. find y". 2 (1- 1)2 12+t (1-1)2 2t (t-1)3 O 1+1 t-1

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Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 2. z = In(2x² + y); x = /i, y = 12/3…

A: Given: z=ln(2x2+y);  x=t , y=t2/3To find:dzdt=??

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: 2. Show that the Euler-Cauchy Equation Iy" + axy + by = 0, 1+0 can be transformed into the constant…

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Q: 7) Suppose w=rt+rs' and r= tan-' (2x² +3y), s=x²y' +3y and t = x²y² .Use the chain rule (from…

A: Given w=r2t+rs3r=tan−1(2x2+3y)s=x2y3+3yt=x2y2

Q: 32 Q3: If f(z) Find the residues at all the poles of f(z) !! (Z+2)2(Z2-1)

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Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

Q: 9. Verify that p(t) = te/50 satisfies the condition p(t) dt = 1

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: Obtain the TSE of h(t) = 2t (1+t)¯¹ in powers of (t – 1). - O-1 + ½(t-1)-(t − 1)² + ½ (t− 1)³ – ½⁄(t…

A: As per the guidelines  I am answering only 1 question.

Q: Find for x = x(t) defined implicitly by 25+25 x In(t) = e25xt Also evaluate dt at (t, x) = (1,1).

A: Given,25 + 25xlnt = e25xtTaking 'log' with base 'e' on both side, we getln25 + 25xlnt = lne25xtln25…

Q: If Σ An diverges then > can diverges O only if c>0 O only if c< 0 O only if c+0 O for any real value…

A: Given, the series ∑an diverges, then we have to find the values of c for which the series ∑can…

Q: Compute analytically convolution of x(t) and h(t) defined as follows: S 1, if 0 <t< 2, { 0,…

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Q: az az and as Use the chain rule to find at (=) Z = tan V u = 8s + 5t, v = 5s – 8t az as az at

A: Topic:- derivatives

Q: 2 2 If z = f(x, y), where x = s² - t² and y = t² s² and z is differentiable, then - Select one: True…

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Q: 2. Two ponds are connected and fed by a single stream flowing through them. Pond A holds 500, 000…

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Q: 11. Show that the Beta function, defined by B(x,y) = (1-t"-1 dt , for x> 0, y > 0, satisfies the…

A: the given function is βx,y=∫01tx-11-ty-1dt for x&gt;0,y&gt;0 substitute t=1-s therefore, dt=-ds when…

Q: If Saz dy = In|ly +1- Inly +2| + c, then S- %3D y2+3y+2 dt = e2t +3et+2 In(e' + 1) + In(e + 2) + c…

A: The objective is to find the correct option

Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: t²x"" +2tx" + x' +2022x 0 for t> 0. If their Wronskian satisfies W(2) = 20, then find W(t) for all t…

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Q: Assume that after w months, butterflies’ populace in 1000 is calculated as: f(w)=12w+cos⁡(16w)+n×100…

A: Given: Butterflies’ populace after w months is given by f(w)=12w+cos⁡(16w)+n×100 in 1000 where n=824

Q: ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

A: Find your answer below

Q: 2. Evaluate ř(t) dt: 4 4t ř(t) t2 + 5t + 6' î + 2e4t cos t j - k; a = 0 and b = 4 t2 + 1

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Q: SSS zdV Q3: Evaluate E + y² + z² = 1 and x² + y² + z² = 4 in the upper where E lies between the…

A: We have to evaluate the integral ∭EzdV, where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4…

Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: Let f(x, y, z) = In(x² + z) + y²e#². Find fzyæ-

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Q: Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less…

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Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy =yx.

A: Since, yz = zxy

Q: Solve the DEQ given the initial condition (4,-2). Graph it on the slope field. 10 9 1 8- Let…

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Q: Suppose z = 2xy where x = t^2 + 1 and y = 3 - t. Use the chain rule to determine which of the…

A: In the given question the functions are given as z=2xy , x=t2+1 , y=3-t . The objective is to find…

Q: 1. Find the linearization of r – z at a = 2.

A: Find the linearization of x3-x at a=2.

Q: Suppose that x2 = y2 = e and yz = zxy. Show that xy = yx.

A: Assume that x2 = y2 = e and yz = zxy.  Now from  yz = zxy we have  yz-1 = zxy-1z-1y-1 = y-1 x-1 z-1…

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

A: