Let a = (x + y)i + 2j + yk and b = 3i+ (4.x + y + 1)j + 4k. Find values of x and y such that a l b. Find values of x and y such that a || b. (Hint: Assume that ca = b for some value c.)

Q: 1. Express the followings in the form of x + iy where r, y E R.(choose one.) (a) 금+ 부 (b) ( + ) ( –…

A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

Q: Let T: RP → R be defined by T() = Aã where -2 3 11 A = 1 -2 1 -1 -3 4 and let 6 %3D What is the…

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Q: Let f(2)= ¹5 and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of…

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Q: (1) Find an element r E D4 such that DaH R90 = V. %3D

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Q: D Express the interval in (a-k, a+R) aad 1 x.-alc.R I(3x+1)?(<!

A: |(3x+1)2| &lt;1 both side we take square roots |3x+1|&lt; +1 3x+1 &lt;+1 3x+1&lt;1    or    3x+1&lt;…

Q: Let a = 1-j+ k, b = 4i + 5)-k, and c - -I+j+ 4k. Find the Indicated quantity. a (b x c)

A: Given: a=i-j+k, b=4i+5j-k, c=-i+j+4k To evaluate: a·b×c Cross product of two vectors r→=ai^ +…

Q: Given f(x, y) = 12/8x* + 6y + 2xy°, find f. (x, y) = f,(x, y) =

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Q: Which of the following expressions is not well defined? Select one: -5 dzf(x,y, z) O b. da 2 dy f…

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Q: The evaluation of S z dx is V4+x2 O In(sece + tan0) + c o - In(sec0 + tan0) + c c In|sece – tan0|+ c…

A: we have to evaluate the following integral .

Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

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Q: Find c1, c2, and c3 such that the rule  0∫1 f(x)dx ≈ c1f(0)+c2f(0.5)+c3f(1)  is an approximation…

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Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: Let A = {x E Z: 8x} and let B={rEZ:12lx}. Then * ACB ВСА None of these A=B

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Q: Evaluate and simplify y'. In x where a is constant y In x + a

A: Given:   y=lnxlnx+a

Q: Q5: For which values of z is w =1/(z – i), defined? For these values obtain and v and evaluate w…

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Q: Find all values of x and y such that Px(x,y) = 0 and P Py(x,y)=0 simultaneously. P(x,y) = 5x² -…

A: Topic = Algebra

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

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Q: Q5.Given that W = f(x.y.z)% x+2y+, find : aw aw in terms of s and r, if and x=, y=r +Ins, =2rr.

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Q: Given the multiple variable function f(x, y, z)= Ax*e» - Bz cosx*y°)+Cx*y*z?, where the coefficients…

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Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: Detemine the x-values at whìch, 9水)= 2xー 3xー+X メt,xE - スxナラメー3x underined. Evaluate the linit ac…

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Q: Find values a, b, c, d such that the function (x+ 1)³, -2 < r <-1 s(x) = { ar³ + bæ² + cx + d, -1 <…

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Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

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: a) Find as when s = 1,t = 1 for f (x, y) = x³ – 3xy - 6x + 6y,x = 2t + s, %3D %3D y = 2s - t.

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Q: Find a, b > 0 such that the following equality holds: {r €R : -a < br – 3 < v2} = [-3, 3).

A: Note the result : The set can be represented in interval form as .

Q: If f(x, y) = (2x? + 8y²)í, then f_(0, 0) = %3D A) 0 В) 1 C) 4 D) 2 E) Does not exist

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Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: Given f(x, y) = In Vay³. What is the value of fy (1, 2)? If the answer is a fraction, write your…

A: Given:  fx, y=lnx2y3 To Find:  To determine the value of fy1, 2.

Q: Let f(x) = a2 +1, g(æ) = Va+3, h(x) = 4 (go(hof))+(gof) at x=2? %3D Find I-4

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Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: . Evaluate F dr, where F(x, y) = ryi+z'y²j, and C is given by r(t) = ti+tj. 0sts1.

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Q: (iii) Given that |f(x, y) = e* sin(y) + x²y² = y + 10 a² f əxəy af ax Determine dx and Type your…

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Q: Let f(x)= x+1, find all xeR such that f[f(x)]=2 the solution set is: а. у%3D0. b. y=x. с. у#х. d.…

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Q: Q5: For which values of z is w =1/(z - i), defined? For these values obtain u and v and evaluate w…

A: Given that: w=1z-i, z=1-2i

Q: 1 f f(x) = : R → R, Vx2 – 4 At how many different integer points x is discontinuous? 25 - O A) 3 O…

A: We have f(x) = 1x2-4Clearly f(x) assumes real values for all real values for all x except for the…

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

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Q: Evaluate F· dī where C F = = , and C is given by - T(t) = , 0 < t < T 0 <t<

A: Given

Q: x'y=x'+ xy. linear DE Which value of k, the given DE will be homogenous?

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Q: O Consider K points x1,..., X € C. Show that 0;x; € C, for >0; = 1,0; e R i=1 i=1

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Given f(x,y)=x-exy, evaluate fy(3,0). 06 O 27 O 9 O 13

A: topic- partial differentiation

Q: Use the algebraic definition to find ix w if i = 2i + 2j – 3k and w -2i +j- 3k. - %3D i x w =

A: Given: v=2i+2j-3k And, w=-2i+j-3k

Q: Given f(x, y, z) = In(x² + y? + z?), show that 2 dy? d22 x2 + y2 + 22

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Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = 3x3 −…

A: A function's partial derivative z=f(x, y) can be determine by differentiating z with respect to…

Q: - (3x + )*. Let y Then - A(Ax + +)" (8 -)", where B dy = Al 8x + xp A = B = C = D = I| || ||

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Q: Let *- y= ÿ.z=0 and x ỹxz= V3 where x,y,ZER'. Which of the followin. 2 can be the value of X Z? V3…

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Q: Write a in the form a = arT + an N at t-0 for R(t) = t2i +

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Q: II. Let U = R, { x € R | 26x + 25x = 0}, J = { x €R | |4x + 2| > 10 } and K = { x € R | x? – 3x – 4…

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