T: P2 → R³ defined by T(a + bx + cx²) = (a + 1,6, c). T: R5 → R² defined by T(x1, x2, x3, X4, X5) = (x1,x2). T : R' → R defined by T(7) =< ¤, (1,2, 3, 4) >.

Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: Calculate r' (t) and T(t), where r(t) = (6 +5t,9 – 61, 2t). r' (t) = ( ). T(t) = ( ).

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Q: of of Find and f(x, y) = x 3 +3x 2y- 9xy 3 4-32 + 2xy - 9y3, - 3x2 + 3xy2 *=x2 + 3xy - 9y3, 4 = 3x2…

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Q: Let f(x, y) = 5e*" and c(t) = (2r², r³). Calculate (f • c)(t). Use the first special case of the…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 3t³i + 6tj - t²k (a) r(t) (b) r"(t) (c)…

A: Given data÷

Q: Suppose z = x² sin y, x = s² + 3t², y = 6st. Əz Əz A. Use the chain rule to find oz and 0 as…

A: Suppose .(A) By using chain rule to find  as functions of .(B) To find the numerical values of  when…

Q: Find f '(2), where f (t) = ü(t) · i(t), ü(2) = (1,2,–1), ū'(2) = (3,0,4), and v(t) = (t, t?,t3).

A: To find out the f'(2)

Q: Suppose z = x² sin y, x = -4s² + t², y = -2st. A. Use the chain rule to find and as functions of x,…

A: Given:The functions .To find:The values of:a) b) The numerical values of  at .Concept Used:Power…

Q: If r(t) = , find r '(t), T(1), r ''(t), and r '(t) ✕ r ''(t).

A: Given  r(t) = &lt;4t, 6t2, 2t3&gt;

Q: (*) Y(z) 16z (2²+1)(4z-1)(2z-1) Now partial fraction is 16z 112 96z 16 (z²+1)(4z-1)(2z-1) 85(+1)…

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Q: 2 -JM 3 0 5 Determine whether v is in the range of T. Fully justify your answer. 1 -2 -1 Let A = =…

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Q: Зху? — 3x nint of r

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Q: Find r'(t), r"(t), r(t) r"(t), and r(t) x r"(t). r(t) = 32²1 - 4tj + 12³k (a) r(t) (b) r"(t) (c)…

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Q: a) If L-{F(s)} = f(t) and L-1{G(s)} = g(t), and if a and B are constants, then L-1{aF(s) + BG(s)} =…

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). That is; f(t)=L-1[F(s)]

Q: What is t' (x) when t(x) = In( ): %3| 2x2+3x+2 Select the correct answer below: O t (x) = 2 + 4x+3…

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Q: Let T: R³ R² be defined by T (E) 2x1 -2x2 + x3 Ex: 5 +2₂] -3 ---(~- -[:] ·~ -E] ·~ -E] --²-(~-…

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Q: (4-.1.P)an (4-t,t,) and V(t) = (3, t,

A: The given curves are ut=4-t2, t, t2 , vt=3, t2 , t . Let vt=vs →3, s2 , s . Comparing  the…

Q: P(x1, #2) –X2, Q(x1, x2) = x1; D = {(x1,x2) :0 < x1 < 1,0 < x2 < 1}. = -

A: Note : " As per our guidelines we will solve only first question . If you want any specific question…

Q: Given r(t) g(t) find: r (0) h(t) find:r (1) find:r (2) find: r (3)

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Q: If r(t) =  , find  r'(t), T(1), r''(t), and  r'(t) × r ''(t).

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Q: P(x1, x2) = x1X2, Q(x1,x2) = –2x102; D = {(x1,x2) :1 < x1 < 2,0 < x2 < 3}. %3D

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

Q: Let F(2) = f(x) and G(x) = (f(x)) - You also know that a = 2, f(a) = 2, f'(a) = 7, f'(a³) = 15. Find…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). r(t) = 2t²1 - 4tj + ²t³k (a) r(t) (b) r"(t) (c)…

A: Note that, according to Bartleby guidelines, we can answer only the first 3 sub-parts in the case of…

Q: Use the general chain rule to find DH (1,-1) given G(U)=G(u, v) = and H(U)= F(G(U)). /u²+3v² +2 F(X)…

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Q: If f(x, y, z) = 2x5 + 3y5- 8x2y?z?, what is the partial derivative of f with %3D respect to z? fz =…

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Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: Find the saddle point/s of the function f(x,y) = x + y² +x²y+4 O a. (E ,-1) & (- 2 -1) O b.(4,0) &…

A: Let's find.

Q: Find r'(t), r"(t), r'(t) r"(t), and r'(t) x r"(t). 1 t³ k 2 r(t) = 3t²1 – 3tj + 2 (a) r(t) (b) r"(t)…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 5t²i - 5tj + 3t³k 2 (a) r(t) (b) r"(t)…

A: Note: As per the guidelines, I have solved three sub-parts. If you want the solution to the last…

Q: Consider f(z, y) = z² + y³ and g(x) = (x, x², z³). .Then D(g(f(x)) %3D O 1× 3 О Зх1 O 2 x1 О 1x2 O 5…

A: consider f(x,y)=x2+y3 anf g(x)=&lt;x,x2,x3&gt;we have to find the dimension of matrix…

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: dz (е) dz

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Q: Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for…

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