- T:(x, y) → (x, y – 2). What is the preimage of (3, 5)? b. (3, 7) a. (5, 7) с. (3, 3) d. (5, 3)

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

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Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

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Q: Find the nullity of T.T: R4→R2, rank(T) = 2

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Q: ди ди ди for u = az Find p-q if p= x+ y+ z ,q = x + y + z ,r = = (V3,2,1). and ax' əy 9-r x + y - z…

A: Q3. Given that                                            u=p-qq-rp=x+y+zq=x+y+zr=x+y-zPoint, (x, y,…

Q: b) %3D Difleventiating both sides writ sc on dy %3D doc Applying chain rule; dy d. du du doc de U =…

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Q: derrorsinx,y,zbe0.001.Find relative error when x = y = z = 1.

A: Given,                 U=z4                                                  ...(1)  x=y=z=1, and…

Q: for: m -} answer fx) = x2-x at x=-1 anjwer for: 4-4, = m CX -X,) dy dx m= m- 2x-X m = 26)- (-1) m=…

A: Given:        f(x)=x2-x  at x=-1 This is in the form of y-y1=mx-x1    y-intercept form at x=-1 is…

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): = 历 内 z = x²y +…

A: Here given that                       z=x2y+xy2,  x=3-t3,  y=3-t6 We have to find dzdt by using…

Q: Q4: 16 u. nin N, then 5 bounded fo belongs t and infinum

A: We define a subsequence  an = Sin(pi/2) + (-1)n = 1 + (-1)n . So, a2n = 2 and a2n - 1 = 0.

Q: Let f(x, y) = 9e2xy what is fxyx (x, y) =? %3D Select one: O a. 72ye2xy + 72xy²e2xy O b. 36хуе2у +…

A: Given: f(x,y)=9 e2xy ; To find the value of fxyx(x,y)=?

Q: det TiP M,2 be defined by -Q,X + QX + agX ). Show that ī is a linear transforimation and find T…

A: The solution is given as

Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: Let -2xy – 3yz – cz, x = st, y= e", z=t? Compute ди (4,-5) = ds dw (4,-5) =

A: The given function.

Q: t-4 - Given s(t) find s'(t)- t+3

A: st=t2-4t+3 take derivative s'(t)=ddtt2-4t+3 use the quotient rule fg'=f '·g-g'·fg2

Q: 5. Consider the false statement Vr, y E Q, x < y = A counterexample is a = -1 and y = -2.

A:

Q: - (19,8) (10,0) (19,8) ) Show that So fdx + gdy = Sao.0 24x?y dx + 24y2x*dy is independent of path:…

A: Let's find.

Q: Q3. Let A = {(r, y), 4x² + 9y² < 36} C R² Is A connected? pathwise connected? Justify your answer.

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Q: The transformation (x, y)(-x, y) reflects the preimage across the diagonal line y = x. O True O…

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Q: 3. Show that S4 has the presentation (x, y|x* = y² = (xy) = 1). %3D

A: To show: S4 has the presentation x,y| x4=y2=(xy)3=1

Q: dw ,s = 1 If w = 2x? ds + y, x = 2 - s, y = 1+ 2s², then by chain rule when %3D సా | 8

A: See the attachment

Q: (b) Find fx, fy and f,if f(x,y,z) = zln(x²ycosz). (c) Use chain rule to find du and 2 if z =;x =…

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Q: Let h(t) = 3t3.2 7t-3.2 %3D | Then h'(t) is h'(1) is s! (7),.4 and h''(1) is

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: Q3: van fy = xy*-1 + x",In(x) f(x,y) = x +y* • if it was True false

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: Compute the length of the path r(t)= (t, 4t3/2, 2t3/2) over the interval 0<t<8.

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Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: Fin d the sc cond soluhen prr tk edo te edo If Konow that y, =x IS a solotień

A: We will reduce the order of the given given second order homogeneous differential equation using the…

Q: +3 fn d the deivotive of this funckio slape of the tonpent On d the line ot (4,1).

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Q: S Integrate the fallowing functinne the given aver R: y24x-x² and y-X

A: Integration of the function

Q: 5) s how that the line of intersection f the Plas and 5x-2y-Z=0 is Parrliel to theline X+2y-22= 5…

A: Given that plane  ,P1:x+2y-2z=5plane , p2:5x-2y-z=0line ,l:x+32=y3=z-14Normal of P1  ,…

Q: if y=Asinx+Bcosx then prove d2y/dx2+y=0

A: Given,

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: Use the Chain Rule to find ôz/əs and əz/ðt. z = tan(u/v), u = 4s + 7t, v = 7s – 4t Əz as az II

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Q: -E- x2 and S: R2 → R², 4. Let T : R² → R², x-y (a) Find (SoT)(u) where u := E R?. (b) Find a…

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Q: {(x, y), 4.x2 + 9y² < 36} C R2 ected? pathwise connected? Justif

A: Connected and path connectedness

Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

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Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

A:

Q: If r(t) = (V10 – t, In(t – 1) - then the domain of r is

A: Domain = (1, 10]

Q: Q2- By using Chain Rule, find au/ax, du/dy, du/az at (x, y, z)=(√√3, 2, 1) u= p-q 9-r' p = x+y+z…

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Q: _et f(x, y) = xe - x². Calculate fx (x, y) and Jy (x, y).

A: To find the partial derivative.

Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

A:

Q: a the diagram, PU||QT, Ì = 42°, RQS = 82°, = v, UPT =r and QPT = x+40°. Prove that PT|QS. %3D P…

A: Given: PU||QT Concept: Pair of interior angles on the same side of the transversal are supplementary

Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

A:

Q: 11 f(x,y) 3x-7y+2, R is the rectangle with opposite car- ners (-1,0) and (1,3).

A: 12. Given: fx,y=2x+2y+2 and triangle with corner 0,0 To find the area of the triangle. The formula…

Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: c- Verify Clairaut’s Therom f(s,t) = s²t + In(t²-s)

A: In the question it is asked to verify Clairaut's theorem for the following function given in…

Q: Use the Chain Rule to find az/əs and əz/ðt. z = (x - y)7, x = s?t, y = st? əz as əz at II II

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Q: Use the chain rule to find where First the pieces: End result (in terms of just t): d = 江 西 血麵| 2 =…

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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.