3. • Use sequential continuity to show that any polynomial P(x) = x" + a,n-17"-1+...+ ao %3D is continuous from R to R. Give an example of a polynomial that has no zeros in R

Q: Use the Laplace transform to solve the given initial-value problem. y" + y = 2 sin(V2t), y(0) = 11, ...

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Q: Given the differential equation, its particular solution, and its wronskian x3y" + 8xy' + 12y = 6 x5...

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Q: Problem 4: Define f: [0, 1] R by f(x) = 2x if x is irrational and f(x) =-1 if x is rational. Careful...

A: Given function f: [0, 1]→ℝ f(x) = 2x , when x is irrational-1 , when x is rational

Q: Problem 4. Let A be an nx n matrix and S = {v1,. ., Vn} be vectors in R" such that Avk = \gV¢ for k ...

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Q: For a maximization problem we know we have reached the optimal solution when all the (Cj - Zj ) row ...

A: In simplex problem, we calculate Cj-Zj  For the maximization problem, the value of Cj-Zj is negative...

Q: The polynomial p(x) = 6x4 - ax3 - bx2 + 28x + 12 where a and b are constant, has factors (x+2) and (...

A: The given polynomial is p(x)=6x4-ax3-bx2+28x+12 since x+2 is the factor so x=-2 will make the polyno...

Q: 5. Use the finite difference method of order two with step size h = 0.25 to solve y" – xy' – xy = 0,...

A: solving above question using second order finite difference method 

Q: 6) (ii) Consider the collection of subsets of R given by B= {[a,b]|a E R, b E R and b > a}. Can this...

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Q: QUESTION 4 Solve the following integral by using substitution method. S(6- sin3x)' cos 3x dx.

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Q: Qz) if the vechri Find ū =-i +J and ū =Jz ie JJ J +2 Ŕ a) The scalev component of ū in the divection...

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Q: 5 If g(1) = 4, g(5) = -7, and | g(x) dx = -8, evaluate the integral ag (x) dr. Answer:

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Q: A particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point (1,2,...

A: Introduction: When a force is acting upon a particle and there is a displacement, the force works on...

Q: (ii): f(t) = sin (t + 7)+ e³' cosh 5t

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Q: Determine whether or not the given set of functions is linearly independent on the set of all real n...

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Q: Is it possible for a matrix to be both upper triangular and lower triangular? Oa. Yes O b. No

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Q: 1 7 -3 at is tr 2 -1 -8 3 -3 5 wer:

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Q: following figure:

A: The given two angles ∠COD and ∠EOD have common vertex O and common arm OD  

Q: Q5) Describe the Null A by listing the vectors that span the Null space. 135 0 A= 014 -2

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Q: Let an be the nth term o structed by including the

A: Given, an be the nth term of the sequence                    1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, ...

Q: The 26-N force P is applied perpendicular to the portion BC of the bent bar. Determine the moment of...

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Q: ralues are positive or zero

A: for the solution to be optimal, in the minimization problem for the simplex method, depends on the v...

Q: 2. The system of equations log. (r? + y) – 1 +y = 0 Vỹ + ry = 0 %3D has a solution close to (r, y) =...

A: The given problem is to find the approximate solution for the given system of equations using newton...

Q: Given the following set of discrete data in Table 2. Table 2 0.2 0.3 0.4 0.5 0.6 0.7 f(x) 1.0832 1.1...

A: Introduction: The central difference approximation is a better way to approximate the derivative of ...

Q: (TA~ F) F) v (T

A: A logical operator on mathematical statements is a word or combination of words that combines one or...

Q: Solve the equation for x, give EXACT answers,

A: the given equation is 5+2lnx=4 subtract 4 from both sides 5+2lnx-5=4-52lnx=-1  

Q: 3 a) v16 + V8

A: # We are entitled to solve one question at a time ,please resubmit the other question if you wish to...

Q: Find the equation of the tangent line to the curve f(x): at the given point (-5,5) x+4

A: The given problem is to find the tangent line to the curve f(x)=x/(x+4) at the given point (-5,5). W...

Q: 2) From a deck of 52 playing cards, 5 cards are to be drawn. How many sets of 5 cards are possible i...

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Q: A metal sheet is situated in the xy plane so that the temperature T = T(x, y), in degrees Celsius, a...

A: Given: A metal sheet is situated in the xy plane so that the temperature T = T(x, y), in degrees Cel...

Q: The matrix for changing coordinates in the Euclidean basis for C4 into coordinates in Cthe jden ot u...

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Q: Use the two properties L1 and L2 to show that the following are linear transformations. (b) T:R² →R'...

A: To show that the given transformation is linear: T:R2→R3 defined asT(x,y)=(−y,x+y,3x−4y)

Q: The solution of e = -has the form x + i (y + 2nn) where n is an integer. What is the value of x? Wha...

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Q: QUESTION 11 Identify the law of logic used in the following simplification step: a. Annihilation law...

A: Given: ¬p∧q∨¬p∧q≡¬p∧q To identify: The law of logic used in given statement.

Q: 14x10 1. The velocity of a rocket is given by v(t) = 2000 In |-9.8r,0sts 30 where [14×10ʻ – 2100r v ...

A: Introduction: The acceleration of an object is determined by differentiating the velocity function. ...

Q: QUESTION 19 Match the set operation with its definition. B ANB B AUB 8 AC a. {x|x €A and x EB} b. {x...

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Q: 4. Solve the differential equation by the method of undetermined coefficients. (Section 4.4) у" - 16...

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Q: Solve the inverse Laplace transform: 3s s2+4s+13

A: We need to find L-1{3ss2+4s+13}

Q: Each of the following linear transformations T is diagonalizable. For each transformation, determine...

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Q: 3. Let d(x, y) := |2 - 2| for x, y E R. . is a metric on R. Show that (R, d) is not a complete metri...

A: Cauchy sequence: A sequence x1, x2, x3, ... in a metric space (X, d) is called Cauchy if for every p...

Q: John is 1 m tall, Hashim is! m taller than John. How tall is Hashim? Mr Tan had 5 m of cloth. He use...

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Q: Which system of inequalities is represented by the graph? [y-x B. C. D.

A: The two bold lines drawn in the graph is represented by the following equations.

Q: 4. Simplify the following: Note: m=2 n=7 (x³ y* z=7)(m+4) x" Vy4 z² (x³ y6)0 х3 у -2 z7 х уZ

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Q: Six equal rods AB, BC, CD, DE, FE and FA are each of weight W 6. and are freely jointed at there ext...

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Q: e drawn to circle O fror C = 4. Find AD.

A: # We are entitled to solve one question at a time please resubmit the other question if you wish to ...

Q: Give integers p and q such that Nul A is a subspace of RP and Col A is a subspace of R9. 1 2 3 4 A =...

A: Introduction: The null space and the columns pace are very important in the theory of matrices. The ...

Q: convert to polar form: a.) √2 (160)sin (wt+30°) b.) 20sin(377t-90°)

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Q: For the following pairs of functions, determine which function grows faster. f(x) = 6x – 5a² + 9, g(...

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Q: 12. From the data below, compute for the standard time if the allowance factor = 15% (added to its n...

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Q: Given X = (R, Tstd) and Y = in the subspace topology. (IR, Tstd), draw and write down the set descri...

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Q: EVALUATE cos (bx/") dx CoS

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