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Question 16 (4 points) How many polynomials of degree 4 are there in Z_5[x]? A/ Question...
C1=5, C2=2 C1 a. How many monic polynomials of degree two are there in Zc[x]? b....
C1=5, C2=2
C1 a. How many monic polynomials of degree two are there in Zc[x]? b. How many polynomials of degree two are there in Zc-[x]? c. Is x2 + 4x + 5 is reducible over GF(p), where p is the largest prime <C?
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using...
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of degree 0 and 1,
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of...
Determine the polynomials each with a degree of 4. Below are the graphs of 3 polynomials,...
Determine the polynomials each with a degree of 4.
Below are the graphs of 3 polynomials, each of degree 4. Determine the polynomials 3. 50 50 40 30 20 30 20 10 t0 10 5 4 32 10
all odd degree polynomials have at least 1 real root. Explain how we can be sure....
all odd degree polynomials have at least 1 real root. Explain how we can be sure. (the x-intercepts of a polynomial are the same as its real roots. Consider the “end behavior” of odd degree polynomials)
(1 point) Find the Taylor polynomials (centered at zero) of degree h 2, 3, and 4...
(1 point) Find the Taylor polynomials (centered at zero) of degree h 2, 3, and 4 of f(x) = ln(3x + 7). Taylor polynomial of degree 1 is Taylor polynomial of degree 2 is Taylor polynomial of degree 3 is Taylor polynomial of degree 4 is
Find the Taylor polynomials of degree n approximating
Find the Taylor polynomials of degree n approximating1/(4-4x)for x near 0: For n = 3, P3(x) = _______ For n = 5, P5(z) = _______ For n = 7, P7(x) = _______ The function f(x) is approximated near z = 0 by the second degree Taylor polynomial P2(x) = 3 + 3x - 2x2 Give values: f(0) = _______ f'(0) = _______ f''(0) = _______
Compute the minimum square error for f(x) = |x|/pi (-pi<x<pi) and trigonometric polynomials if degree 1,2,3,4,5
Compute the minimum square error for f(x) = |x|/pi (-pi<x<pi) and trigonometric polynomials if degree 1,2,3,4,5
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x)...
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x) and q(x), define < p(x),q(x) >= p(xo)q(x0) + p(x1)q(x1) + p(x2)q(22). Let p(n) denote the vector space of all polynomials with degree more no than n. (i) Show that < .. > is an inner product in P(2). (ii) Is < ... > an inner product in P(3)? Explain why. (iii) Is <,:> an inner product in P(1)? Explain why. (iv) Consider Xo =...
For the function f(x) = e 2x, which of the following polynomials is the 2nd degree...
For the function f(x) = e 2x, which of the following polynomials is the 2nd degree Taylor polynomial for f(2') at the point I = 0? 1) P(x) = 1-2+x2 2) P2 (3)=1-23 +22 3) P3(x) = 1 - 2.c + 2x2 4) P4(x) = 1 + 2x + 2x2 O Polynomial in 3) Polynomial in 1) O Polynomial in 2) O Polynomial in 4)
)2 is not an integral Q (Hint: the Lagrange-like corollary of the quadratic polynomials in Zafr). (Hint: you do not need to use the Sieve of educible do this. How can you tell whether a low-degree po...
)2 is not an integral Q (Hint: the Lagrange-like corollary of the quadratic polynomials in Zafr). (Hint: you do not need to use the Sieve of educible do this. How can you tell whether a low-degree polynomial is irreducible?) 9. 65 points) Find all reducible quartie (le degre ou) polynominls in Talun. (Ht oot s to consider quartic polynomials with no roots. There are not so many of these-look for a pattern that It suffices them -and such a polmomial...
C1=5, C2=2
C1 a. How many monic polynomials of degree two are there in Zc[x]? b. How many polynomials of degree two are there in Zc-[x]? c. Is x2 + 4x + 5 is reducible over GF(p), where p is the largest prime <C?
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of degree 0 and 1,
3. Let Po(x) respectively. Find the monic Legendre polynomials of degree 2, 3 and 4 using the orthogonality relation f P(x)Pm(x)dx = 0, mn and m,n E N. 1 and P1(x) = x be two Legendre polynomials of...
Determine the polynomials each with a degree of 4.
Below are the graphs of 3 polynomials, each of degree 4. Determine the polynomials 3. 50 50 40 30 20 30 20 10 t0 10 5 4 32 10
(1 point) Find the Taylor polynomials (centered at zero) of degree h 2, 3, and 4 of f(x) = ln(3x + 7). Taylor polynomial of degree 1 is Taylor polynomial of degree 2 is Taylor polynomial of degree 3 is Taylor polynomial of degree 4 is
Q6 (4+3+3+ 6=16 marks) Let Xo, X1, X2 be three distinct real numbers. For polynomials p(x) and q(x), define < p(x),q(x) >= p(xo)q(x0) + p(x1)q(x1) + p(x2)q(22). Let p(n) denote the vector space of all polynomials with degree more no than n. (i) Show that < .. > is an inner product in P(2). (ii) Is < ... > an inner product in P(3)? Explain why. (iii) Is <,:> an inner product in P(1)? Explain why. (iv) Consider Xo =...
For the function f(x) = e 2x, which of the following polynomials is the 2nd degree Taylor polynomial for f(2') at the point I = 0? 1) P(x) = 1-2+x2 2) P2 (3)=1-23 +22 3) P3(x) = 1 - 2.c + 2x2 4) P4(x) = 1 + 2x + 2x2 O Polynomial in 3) Polynomial in 1) O Polynomial in 2) O Polynomial in 4)
)2 is not an integral Q (Hint: the Lagrange-like corollary of the quadratic polynomials in Zafr). (Hint: you do not need to use the Sieve of educible do this. How can you tell whether a low-degree polynomial is irreducible?) 9. 65 points) Find all reducible quartie (le degre ou) polynominls in Talun. (Ht oot s to consider quartic polynomials with no roots. There are not so many of these-look for a pattern that It suffices them -and such a polmomial...
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