Compute r (t) ú(t)

Q: Compute Div(F) and Curl(F): F--(4y-1) i+yj+(-3y) k

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Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: Find the linearization L(x) at x= a. f(x) = x+ a = - 1

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Q: In Exercises 61-67,firstfind f' and then find f.

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Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

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Q: If z = f (u) + g(v), where u = = and v = x ·y. Prove that Q1: x· Zx – y· Zy = y² · Zyy – x² · Zxx…

A: We have z=fu+gv, and u=xy  and v=x.y We need to use the chain rule and prove x.zx-y.zy=y2.zyy-x2.zxx…

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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Q: The linearization at a = 0 to v4 + 4x is A + Bx. Compute A and B. A = B = %3D II

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Find the d. c. of from definition. Vx

A: As per the question we have to find the derivative of the function : f(x) = 1/√x Using the limit…

Q: 2) Use Green's Theorem to compute f F. df where F=(3x +4y) i + 2xyj and C is the triangular path…

A: Use green's theorem

Q: 2) Use Green's Theorem to compute f F df where F=(3x + 4y)i + 2xyj and C is the triangular path from…

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Q: Show that the functions e*, cos x, and sin x are linearly independent using the Wronskian.

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Q: Find f(t). f(t) = 4s [{{1}} + ) u(t-

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Q: Use the Chain Rule to find az/əs and ôz/Ət. z = tan(u/v), u = 8s + 3t, V = 3s – 8t

A: z=tanuv,   u=8s+3t,   v=3s−8tFormula→∂z∂t=∂z∂u⋅∂u∂t+∂z∂v⋅∂v∂t

Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: If f(x) I (t° + 2t + 6) dt 0. then %3D = (x), ,f

A: The function needs to be integrated first and then to the subsequent function we will be double…

Q: 8 Let A = Define T: R-R by T(x) = Ax. Find T(u) and T(v). 0 u= 12 and v = a - 20 1 0 0

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Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: Find f(t). s(s + 1).

A: L-1[F(s−a)]=eatf(t) From first shifting property, L{e^(at)*F(t)} = f(s-a)…

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Q1:- Let T =- where W-N(0, 1) and V~xShow that T2-F(1,r).

A: We know that  The ratio of chi-square divided by its degrees of freedom is called the…

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: let f (x, y) = x² + xy + y². Using the chain rule, calculate %3D af -(u(x, y), v(x, y)) being u = v…

A: Given that                                   f(x, y)=x2+xy+y2 And also we have…

Q: Let T = x²y-xy³ +2; x=rcos0, y=rsin 0. Find and OT at or 20 TAT

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Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: (2) In Exercises 1-3, find fx, fy, and fz. 1 f(x, y, z) = 1 + xy² – 2z? |

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

Q: 2. Use the Chain Rule to find for z = e¤/y where x = st and y = s2 +t

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Q: Compute t a t2 ctan(t)dt. Hint: Note that 1- 1+ t2 (21)- 1+ t2 ftarctan()dt +C %3D

A: The given integral is ∫t tan-1(t) dt

Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

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Q: Find ds/dt if t = sy1- s2

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Q: Using the second fundamental theorem of calculus and chain rule, compute t dt. t+1 dx 2x

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Q: Let T : R2 → R2 given by T(x, y) = (2x + y, x − 3y), (x, y) ∈ R2. Determine [T]αα , where α = {(1,…

A: We will find the images of (1,1) and (1,2) under the linear transformation T and then write them as…

Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: on vectors for t2 0.

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Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

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Q: c) Use the Chain Rule to compute %3D ds se In (c) express your answer in terms of the independent…

A: Here, the given functions are: f(x,y,z)=x4y+z4, x=st2, y=st,z=s2t

Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: Let r(t) = ⟨1, 2t, 3t2⟩. Compute∫r(t) dt.

A: We have given vector r→t=i^+2tj^+3t2k^ Then,…

Q: Let z = f(x, y) and suppose x = 2u – 3v and y = 5u + 6v. Use the chain rule to express dz in terms…

A: x=2u-3vy=5u+6v Now we apply the chain rule  ∂z∂u=∂z∂x·∂x∂u+∂z∂y·∂y∂u Take derivative of x  and y…

Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.