y' = [2 2 2] 2 2 2 y, y(0)= 2 2 2 [For Exercise 8, the characteristic polynomial is p(A) = -A² (A-6).]

Q: u(0,1)= 0, U(1,1)=0, u(x,0)=2x u(x,0)=2 ALE. A Q.4/Answer ONLY TWO, Except (C) (4) Using Lagrange…

A:

Q: Determine x[4] for the given Difference Equation 2x[k + 2]- x[k + 1]+ x[k]= k^2 x[0] = 1 x[1] = 3

A:

Q: 1 If y = V1-x then y' = 2/1-x

A:

Q: From the table find f(0) using interpolating of Lagrange polynomial X -1 0 2 Y=f(x) 2 5 1 O -1 O o O…

A:

Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

A:

Q: Find the derivative of the function. 10) y = (x + 1)2(x2 + 1)-3 2(x + 1)(2x2 + 3x - 1) (x2 + 1)4…

A: Given:        y= x+12x2+1-3

Q: Allow T2(x) be the 2nd degree Tylor polynomial for the following function: f(x)=2+x*e^(5x) which is…

A:

Q: Using Newton's interpolating polynomial of order 2, namely, bo +b,(x-x)+b,(x-x)(*-x) where x, = 0,…

A: Given:   Newton’s method for polynomial interpolation of order two is given as:…

Q: Approximate f' (2) using the given data f(0) = -8, f(1) = -7, f(2) = 0, and f(3) = 19 and the…

A:

Q: What is the x=g(x) that will diverge the root of f(x) = x3 + 4x2 - 10?

A:

Q: The slope field for the equation y'= - +y is shown below On a print out of this slope field, sketch…

A: Given: A differential equation y'=-x+y To find: Solution that passes through  i)0,0 ii) -3,1 iii) -1…

Q: Find the following using the rule indicated (only): i) If f(x) = (6x? – 8) (3x + 2), find f'(3)…

A:

Q: chain rule to differentiate the following 1 y = sec 4 sec* (√x + 3)

A:

Q: Consider the function f(x) = cosa, -, . Construct the Lagrange interpolation polynomial which…

A:

Q: Write a polynomial function of least degree with integral coefficients that has the given zeros. 23)…

A:

Q: Let f(x) = e^x Find the polynomial H3(x) of degree at most 3 such that H3(1) = f(1), H3(2) = f(2),…

A: Given: Consider the given f(x) = ex .Using a (generalized) divided-difference table, find the…

Q: Prove that In( +VI-X²³) = In ( ¹+ √1-x²) sech ¹(x) =

A:

Q: Q1/ The Lagrange polynomial whose curve passes through the following points y(0) = 1,y(1) = 5,y(2) =…

A:

Q: Prove algebraically that  A+A'B'=A+B'

A: We have to prove algebraically that  A + A'B' = A + B' We know that, the distributive property  A +…

Q: Find all residues of the function z (2-2) not including the residue at infinity. "

A:

Q: Orthogonalize {1, t, t²} in P₂ (R) with 1 (f, 9) = ["ª, f(x)g(x) dx. -1 Then normalize each one so…

A:

Q: Let p(x) be a polynomial function of degree n with simple roots r1,..., xn. Show that ) p"(x;) = 0.…

A: Let Pn be a given statement for all natural numbers n. If  i. P1 is true ii. Pk+1 is true whenever…

Q: Find G′(w) if G(w)=3/8w^6+6^4*squareroot of w

A:

Q: Find the residue of - (:- 1)* at its pole

A: