2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...
Find ao and the first five ak's and by's for the following signal. x(t) = 2 + t + t ; <t<tt
Problem #6: Let T:p2 → 2 be defined by T(ao +ajx + a2 x2) = (7a0 + a1 - 7a2) - (a1 + 25a2)x+ 20 x2 Find the eigenvalues of T. Enter any repeated eigenvalues as often as they repeat. Problem #6: Just Save Submit Problem #6 for Grading Attempt #1 Attempt #2 Attempt #3 Problem #6 Your Answer: Your Mark:
• Show that if A(z) = 1x" + ... + x + ao and B(x) = 1.2" + ... +61 + b (A(x) and B(x) are monic polynomials), then the division algorithm works for polynomials in Z[x] • Show with an example that in general the division algorithm does not work in Z[x]. • Given A(x) = 2,10 + 7.06 +34 – 5x3 + 10x + 2 and B(x) = 7.5 – x4 + 5.x2 + 1 (a) Find Q(x)...
6. Use the generating function method to solve the following recurrence relation: with ao 2, a6
6. Use the generating function method to solve the following recurrence relation: with ao 2, a6
Theorem. Let p(x) = anr" + … + ao be a polynomial with integer coefficients, i, e. each ai E Z. If r/s is a rational root of p (expressed in lowest terms so that r, s are relatively prime), then s divides an and r divides ao Use the rational root test to solve the following: + ao is a monic (i.e. has leading coefficient 1) polynomial with integer coefficients, then every rational root is in fact an integer....
Problem #6: Let T:p2 → p2 be defined by T(ao +ajx + a2 x2) = (890 +6a1 + 902) – (a1 + 36a2)x + (20 – 4a2) x2 + Find the eigenvalues of T. Enter any repeated eigenvalues as often as they repeat. Problem #6: Just Save Submit Problem #6 for Grading Problem #6 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark:
1 #6: Let T: P2 → p2 be defined by T(ao +ajx + a2 x2) = (Tao + 381 +8a2) – (a1 + 36a2)x+ 20 x2 Find the eigenvalues of T. Enter any repeated eigenvalues as often as they repeat. em #6:
ao 10 -9 -8 -7 -6 -5 4 -2 - 2 3 4 $ 6 7 8 9 10 Write the standard equation for the hyperbola graphed above. Preview Points possible: 1 Unlimited attempts. Submit
(b) Find ao and a such that the following quadrature formula is exact for linear polynomials
(b) Find ao and a such that the following quadrature formula is exact for linear polynomials