y 1-i X Given: +1 must be an integer. 14 2+1 ; find xy (round up). Answer

Q: Find a Maclaurin series for f(x) = x2 cos x giving the first four nonzero terms and the general…

A: We will use the Maclaurin's Series  f(x) = f(0)+ xf'(0) +(x2/2!) f''(0)+(x3/3!) f'''(0)…

Q: If x,> 8 and x n+1 = 2 - for nEN. Then the limit of x is equal to 21 11 ***...

A: To find the limit of xn :-

Q: Use the matrix 1 0 11 E -1 1 0 0 1 2 to obtain the Hill cipher for the plaintext message "HELP ME".

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Q: Find eijen values and eigen vectors 5 For M = 5 QNO:7 7

A: We need to find eigenvalues and eigenvectors for , M = 5775 For finding eigenvalues we need to find…

Q: Let H be a subgroup of all automorphism of a field K.then the fixed field of H is a subfield of K.

A: Given: H≤Aut(k) To show: H is a subfield of K

Q: 3. Consider the region D bounded by the curves C₁, C2, C3, C4 oriented as in the following picture:…

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Q: Example 2.33. Evaluate the following (correct to four decimal places) by Newton's iteration method :…

A: (i) To find: the value of 131. Please post the multiple questions separately. Here I answered 1st…

Q: x-y -dA over a square region Using the transformations u=x-y and v=x+y to evaluate R Rx+y with…

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Q: QUESTION 34 In figure P& Q are centres of the • R is the centre of the ci ● ● AB 1 PC

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Q: Consider the function f(x) = x-2 x²-4

A: The given function is f(x)=x-2x2-4. To Examine: Continuity of f at -2 and 2.

Q: Multiply: 7(cos 45° + i sin 45°) and 8(cos 15° + i sin 15°)

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Q: Solve for x: 40 = 3 1 x 3 −1 2 -1 1 -4

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Q: Example 2.40. Solve x¹-5x³+20x² 40x+60=0, given that all the roots of f(x) = 0 are complex, by using…

A: Here we need to solve equations using Lin-Bairstow Method.

Q: Consider the following homogeneous system of first order equations, dx/dt = ax + y, dy/dt = x − 2y,…

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Q: The domain and the range of z=cos-¹(x²-y-3) are represented respectively by OA. D={(x,y) ERXR: x² ≤…

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Q: (A^¬BA¬C) logically follows from A (1) -C (2) -Av-B (3)

A: This is a problem of Logic.

Q: What is the greatest common factor of two relatively prime numbers?

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Q: Example 2.37. Find the double root of the equation x3-x²-x+ 1 = 0.

A: Solution

Q: Is the following set linearly independent or dependent? S₁ = {(1,0),(-3,1)}, O Independent O…

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Q: Prove that

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Q: C Show that dim 9 (√2, 3²/3) = Q(

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Q: For the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A),…

A: The given matrix is,  A = diag(-2, -1, 2). We have to put the following quantities in increasing…

Q: Which one is a geometric progression? 3,12,48,192,... 1,4,9,16,25,... 6,9,12,18,21,...…

A: Solution

Q: f- dx dt - 4x=2e²¹ + e*; where x(0)=0

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Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a horizontal element, the total…

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Q: Activity I. Find the point/s of intersection of each of the following figures given below, draw the…

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Q: Consider the spherical equation given by p = 4 cos sino. Determine its corre- sponding equation in…

A: The relation between the spherical co-ordinate and cartesian coordinate are  x=ρcosθsinϕy=ρ…

Q: Consider the sum S given by 1 S= 1001 + 1 1002

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Q: If a problem is in P, it is also in NP. O True O False

A: All P problems are assumed to be in NP. The following is usually presented as an explanation: We can…

Q: Points D(z), E(2₂) and F(z,) lie on a cir E and F intersect at A, B and C. A, B, C a (a) Find the…

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Q: San Francisco $45 L.A. $100 $45 $25 $75 $80 Denver $20 Chicago Dallas $90 San Diego How many edges…

A: Solution

Q: Find a Maclaurin series for f(x) = x² e-x giving the first four nonzero terms and the general term.

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Q: Consider the sequence of functions {fn}nen, where nx fn(2)= Væ€ [1, 10]. 1+nx (a) Find the pointwise…

A: Given :  fn is a sequence defined by ;  fn(x) = nx1+nx ,  ∀ x∈[1, 10]. To find :  (a) The pointwise…

Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: create 2 sample word problems of integration by parts with solutions

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Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. The y - coordinate of the centroid of the…

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Q: The domain and the range of z=cos-¹(x²-y-3) are represented respectively by A. None of the choices…

A: We have to find the domain and range of z = cos-1(x2-y-3).

Q: Solve the problem Utt = 36uTz u(0, t) = u(1, t) = 0 u(x,0) = 4 sin(2x), PDE: BC: IC: u(x, t) = =…

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Q: Given set U = {1,2,3,4,5,6,7,8,9,10} and A = {x | x is an odd number}. List the elements of set A.

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Q: sin (xy) Which ONE of the following statements is TRUE with regards to lim (x,y) → (0,0) x² + y2 A.…

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Q: 3. y" + 2y' + 5y = t cos(5t) - 6,y(0) = 1, y'(0) = -2

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Q: h- i- d'y dt² -9y=sint; y'(0) = 0, y'(0)= 0, y(0)=0

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Q: Let N and N' be normed linear spaces with the

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Q: Use the Gram-Schmidt process to find an orthonormal basis of R³ that contains a scalar multiple of…

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Q: f (lnx + y) dx − a² dy, where & is the rectangle with vertices (1, 1), 1. Use Green's Theorem to…

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Q: x² The directional derivative of f(x,y,z)=In 1+yz from P to Q(-1,-1,2) is given by... (Correct to…

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Q: create 2 sample word problems of basic rules of differentiation  with solutions

A: First problem: At what rate is the area of square increasing when the side increases at a rate of 2…

Q: If A = {x+|x-1| : xER), then which of ONE the following statements is TRUE? A. Set A has a supremum…

A: Introduction: A set is called bounded in mathematical analysis and related fields of mathematics if…

Q: (D5 − 3D¹ + 8D³ + 16D² – 9D – 13)y = 0 y = (C₁+C₂x)e¯* + С3e* +C₁e²x cos3x +C5e²x sin3x y = C₁еx +…

A: We have given a differential equation ,  D5 - 3D4 + 8D3 + 16D2 - 9D - 13 y = 0 It's Auxiliary…

Q: 8. Given av av 25202v ат +S as² as find a change of variable of S to x(S) so that this equation has…

A: Solution: Given ∂V∂τ=2S2∂2V∂S2+S∂V∂S-V given condition is a change of variable of S to x(S), So our…