Consider a single node x0 and stepsize h. Based on these answer the following: (Q) Derive the formula for Forward Difference method of numerical derivative and show how the error is related to the stepsize h.

Q: Let A = {x x = 12k for some k E Z} Let B = { x | x = 4k for some k EZ} Prove that A CB.

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Q: Give an example of a linear operator TE L(R*") which is not diagonalizable. Justify your answer.

A: give an example of a linear operator T∈Lℝ3,1 which is not diagonalizable. justify ur answer. it is k...

Q: 2. (a) Detennine the nullity and rank ef the following matrix: 1 10 0 0 0 1 -2 0 4 20 0 3 -2 1 2 2 0...

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Q: Find the root of f(x) = (x – 4)° (x +2)= 0, using the initial guesses of X2 = -2.5 and Xy = -1.0, an...

A: Note:- For this problem any particular method is not mentioned. so, here i'm using Bisection Method....

Q: Let f be a function with continuous second derivatives, defined by: 2 = f(r° + y°, 2ry) If we take "...

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Q: Add cx to both sides and devide the equation by c to obtain g(x): x + 2x – 3 = 0 (a) For what c is F...

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Q: Consider the PDE P(z,y) ди +Q(x,y)º ôxôy = 0, +e. where P and Q are polynomials in two variables wit...

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Q: Let A = {x | = 12k for some k E Z} Let B = { x | 2 = 4k for some k E Z } 4k for some kEZ} Prove that...

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Q: 2. Define the map T:P2¬P4 by T(f) (x)=f(x²), Please determine the rank of I by using standard basis.

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Q: An investor has at most $40,000 to invest in government bonds, mutual funds, and money market funds....

A: To determine the amount of money that should be invested in each fund.

Q: Consider the three points A(-1,2,0), B(-4, 5,0) and C(-2,6, –4). You are given that, -3 AB = and AC ...

A: Consider the points A(-1,2,0), B(-4,5,0) and C(-2,6,-4) And Given AB→=-330,  AC→=-14-4 Projection of...

Q: Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane...

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Q: Find the Laplace transform of sinh3 4t

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Q: Determine g' (1) if g(x) = (3h(x) + 4)'/2 given that h'(1) = 4 and h(1) = 7. 0 6 O 6/7

A: given   g(x) = (3h(x)+4)^(1/2) h'(1) = 4 , h(1) = 7 , determine g'(x) = ?

Q: In what direction from the point (1,-1) is the instantaneous rate of change of 22 f(x,y) = 3x* – 10x...

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Q: Find the length of the curve with parametric equations x = e' · cos t, y = e' sin t, with 0 <t < 2nT...

A: Given x = et.cos(t) y = et.sin(t)

Q: Suppose V is finite-dimensional, T E L(V) has n = dim V distinct eigenvalues, and S E L(V) has the s...

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Q: Q2/ Solve the differential equation by using the appropriate method y' = (y + 4x)2

A: Formulas of the differentiation and integration ddxxn=nxn-1∫xndx=xn+1n+1+C∫1x2+a2dx=1atan-1xa+C

Q: (A v B) -> "C CvD ~В -> А А -> D

A: We will use deduction method.

Q: Q1 Assuming that the equations in Exercises 25-26 define y as a differen- tiable function of x, use ...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

Q: Write an equation for the polynomial graphed below 4- 3 -2 -1 -5 2 3 4 5 -2. y(x) =

A: To write the equation for the graph of the given polynomial.

Q: Use an appropriate series in (2) in Section 6.1 to find the Taylor series of the given function cent...

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Q: 11. Let S = Show that u= 1 E span S. 2

A: We have ,  S = { (1,-1,0,1) , ( 1,-2, 0 ,2) } And  u = ( 0,0,1,0 ) (.) span S contains all that vect...

Q: 2U y'sy tan(x) 2) yy's 2Xes

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Q: Given y = 4 cos(x) - x. Determine where the function is increasing in [-2, 7]

A: Given y = 4 cos(x) - x

Q: Compute f dx, where f(x)=|x |

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Q: 3y"' + 2y" = 0. y(0)=-1,y'(0)=0,y"(0)=1 Solve this

A: First of all write the characteristic equation of given differential equation and solve it for root'...

Q: One solution of the differential equation is given. Find the general solution. y)-y"-12y'-40y 0, y e...

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Q: #1. Use mathematical induction I to prove that for all integers n 2 3, 2·3 + 3 · 4 +. + (n – 1) · n ...

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Q: 2016 What is the highest power of 15 that divides | 1000 Be careful! 15 is NOT prime.

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

Q: Based from a study to a certain player using Ald in Rank Game, the No. of Stack collected by the her...

A: The Lagrange's interpolation formula is given by  fx=x-x1x-x2x-x3x-x4x0-x1x0-x2x0-x3x0-x4y0+x-x0x-x2...

Q: Find the coordinate vector of p relative to the basis S = {P, P2, P3} for P2. %3D p = 20 – 30x + 25x...

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Q: Given a point in spherical coordinate (5, ) find its equivalence in cylindrical coordinate. Draw the...

A: Introduction: Apart from the rectangular coordinate systems, there are two other coordinate systems ...

Q: Matrix B:

A: Given two matrix A and B  ,we have to find the value of A-B.

Q: The PDE x =0 is ax (a) Hyperbolic for x>0, y0, y>0 (b) Elliptic for x>0, y0

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Q: press each statement in “if-then” form.   1.     Every multiple of 4 is a multiple of 2. 2.     W...

A: Given statements 1.     Every multiple of 4 is a multiple of 2. 2.     When a – b is a positive numb...

Q: Differentiate a circle from a parabola?

A: A circle is (geometry) a two-dimensional geometric figure, a line, consisting of the set of all thos...

Q: 11. Let S= {| -2 }. Show that u= E span S. 1 2

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Q: Let T E L(F<") such that T( for any z, w E F. (a) Find all the eigenvalues of T and their correspond...

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Q: For each of the following, draw possible diagrams that match the given measurements. Then calculate ...

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Q: 3. Show that the largest value of o that can be used for some e > 0 if lim (2+ 5x) = 17 is エ→3 anx" ...

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Q: Express the answer of the following problems in form rciso with and -Tss下 O Z: I+i 1-i3

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Q: (9) For any eigenvalue 2 of the nonsingular matrix A with any natural norm, then (a) || A || S| 2 |S...

A: We have given four choices.from those,the correct answer is option(c)

Q: 2. Fill in the blanks Let y be a solution of the differential equation y' = , where – 1<x < 1, -1< y...

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Q: (x2D2 - 3xD + 41)y = 0, y(1) = -n, y'(1) = 2n %3D

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Q: find the apPhto Ximation of the follou) values, which Ts different between the intesors 22/7 da 2+ s...

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Q: 5 0.6 0.1 Apply Gershgorin's theorem on B = -1 6. -0.1 1 2

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Q: a. Write the equation of the line that represents the linear approximation to the following function...

A: Given that  Function f(x) =x/(x+2)  To find the linear approximation

Q: 2z x(z) = 2 1 2

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogo...

A: Given vectors are y=466−1, u1=1101, u2=−120−1 and u3=−1011. We have to write the vector y as a sum o...