Calculate (aijkXiXjXx), where the a¡jk are constants. axi

Q: 2. f(t) = e4"(t² + 3t + 5)u(t) %3D

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Q: Let y = 2x + 2 and t = x + 1.What kind of variation do y and t have? Explain.

A: Given: y=2x+2t=x+1

Q: If u = a + j13 and v = -11 – jb, calculate Im(u + v).

A: Add the two complex numbers then write the imaginary part.

Q: Find proj,u. v= 7i- 3j + k, u = - 4j + 3k 60 45 j+ -k 59 O A. 59 105 45 15 O B. 59 -i- j+ 59 59 21…

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Q: Suppose that f(r, y) = 3x y + 8a? + 4y? then find the discriminant of f.

A: f(x,y) = 3x²y² + 8x² + 4y² So, fx = 6xy² + 16x  &, fy = 6x²y + 8y  &, fxx = 6y² + 16 &,…

Q: M is the midpoint of AB 2x + 1 and MB AM = %3D 1 ond AM

A: Given;- M is the mid point of AB AM=2x+1 and MB=3x-2    Therefore, AM=MB 2x+1=3x-2 3x-2x=1+2 x=3

Q: make outbound JÄ x -4/3B = -12Ã ·B Jän; B A 0 = the corner achieve True false

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Q: Find the approximate value of (5.02)2 + (11.97)² with the help of appropriate linearization.

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Q: Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is…

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Q: Use the one sided Greens function to solve the I.VP. -1 2 In 12, y(1) =0, y'(1)=1 412 y" +8ty' + y =…

A: Given equation is, For solving homogenous equation, By cauchy euler equation,

Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

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Q: Q5) ẩ.ẩ jolve the eẩqẩuatẩionj; 2x²y dy/ldx + 2xy' +1= 0

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: EX: EXPress i w X.+24+2 where. w and. w in termsfu.amal.V. Z24. o..... ...

A: Chain rule: If w is differentiable function of x, y, z and x, y, z are differentiable functions of…

Q: J 5(x) =-J5 (x) ulgn O ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 04. Show that T = satisfies the equation T + Tyy = T³. %3D

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Q: Evaluate dt 13. 1 - sec t

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Q: The Cornev 8-I make outbound A, B. 3. achieve Ax-u38/--12A.B %3D Otrue 2)Err

A: We know that  a×b represent vector product of two vector a and b  a.b represent scalar product of…

Q: Let f(x, y) = 160 2x2-3y² 2a? – For which value(s) of y is f(4, y) = 10? y =

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Q: EX show that 2. J능 (x)

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Q: R V In ORSTV, VT RS = 4(x 3x 1, TS 2х + 1, and %3D 2). Find the value of x.

A: Parallelogram: In a parallelogram opposite sides are equal. In parallelogram RSTV , VT=3x-1, TS=2x+1…

Q: R. 4. Use the information in the figure and prove that VC = CX, making use of reflec- tions. [UCSMP,…

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Q: P is the midpoint of GH implies that GH = 2PG.

A: We have to prove that GH=2 PG if P is the midpoint of GH. Drawing the figure of given condition, we…

Q: A) Eliminate the arbitrary constant/s: 1) 2x³y + xy? 40 %3D

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Q: Why doesn't the constant O have a degree?

A: Given: Zero polynomialp(0)=a0+a1 (0)+a2 (0)+...+an (0)

Q: e where r is jiven peu'ametor! Fnd f'6).

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Q: Find r'(t) = 8Vti + t?Vij + In(z²)k r'(t) =

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Q: There does not exist r E Q ə r² = 2 ylgn ihi

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Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

Q: f. . Prove false by creating a counterexample: 9(AUB) C P(A) U P(B)

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Q: D Find the Constant c that makes f Continyous for a. reql nymbers f6)= %3D

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Q: Į va | Vi(t? + 6t +7) dt. 4. Find

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Q: Differentiate. V(t) = (t + 7e')/t %3D 3 7/)eIn(e) + v7 * V'(t) = 2

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Q: Find partial derivative.

A: We use product rule to find the partial differentiation.

Q: Let z=xin(x2+y2-e4)-176xy, x=te, y=est, If the value of z when s=2 and t=1 is equal to Ae?+Be4, then…

A: Explanation of the answer is as follows

Q: Q2. If ay = aji are constant, calculate a2 (ayx1xj)

A: We have given that aij=aji=constant .So to calculate the given question first we will take partial…

Q: Find projy u. v = 7i- 3j + k, u = - 4j + 3k 105 O A. 45 15 59 '- 59 + 59k 60 45 O B. - 59i* 59k 12…

A: Given vectors are,  v=7i-3j+k and u=-4j+3k The objective is to find projvu Now, u·v=-4j+3k·7i-3j+k…

Q: Use L and L to solue y' t 3y= f4) y)=5, where f4), (32)

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Q: .3 dx J Tx²+9 .2

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Q: t13 dt +C %3D

A: Integration

Q: EXERCISE 4.11.2 ONLY DO (D-F)****

A: For part d: According to the given information it is required to prove that for any positive integer…

Q: Je b. Find of f(x,y) = ye*"? ax' ay %3D

A: Use logarithmic differentiation to solve it.

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Let f(r, y) = 2ry +3x?y2, then fry

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Q: For Exercise, use Cramer's rule to solve for the indicated variable. Solve for y. — бх + 7y = 8 2x +…

A: The matrix of the coefficients of x,y,z is: Then we find the determinant of it

Q: Q1\ why xº = 1 %3D

A: PROOF OF X^0=1

Q: What is UF, where F = Ø

A: Given F is a null set, i.e. F=∅ We need to find the arbitrary union of null set, i.e. ∪F

Q: Q3) If f(x, y?) = x² + y2 + Vxy find : af(x²,y) and f(x?,y) ду

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Q: Let (-) - {. S 8x², x 9 Find the values of a and b so that f will be differentiable at x = 9. а i b…

A: For differentiable function, left hand derivative is equal to right hand derivative

Q: Fs Continuou's True or False ? on [ab], then b

A: