1) Given f(x) = x^2 + x + 1 and g(x) = x^3 + x, compute...

1) Given f(x) = x^2 + x + 1 and g(x) = x^3 + x, compute f(x) * g(x) in GF(2^4) with the irreducible polynomial m(x) = x^4 + x + 1.

1.5) Give the set of polynomials for finite field of the form GF(2 ⁴ ).

Expert Solution

Colby Messinger answered 1 week ago

Let f(x) and g(x) be two generic functions. Assume limx→0(f(x)+2g(x))=2 & limx→0(f(x)−g(x))=8. Compute limx→1(f(lnx)/g(x2−x)). A. It...

Let f(x) and g(x) be two generic functions. Assume limx→0(f(x)+2g(x))=2 & limx→0(f(x)−g(x))=8. Compute limx→1(f(lnx)/g(x2−x)). A. It cannot be computed B. 2 C. 4 D. -3 E. -4

(a) (f ∘ g)(3) (b) g(f(2)) (c) g(f(5)) (d) (f ∘ g)(−3) (e) (g ∘ f)(−1) (f) f(g(−1))

Suppose f(1) = 2, g(1) = −1, f′(1) = 3, g′(1) = 2, f(2) = 1,...

Suppose f(1) = 2, g(1) = −1, f′(1) = 3, g′(1) = 2, f(2) = 1, and f′(2) = 0.2. Calculate the derivatives of the following functions at the provided point (be careful with using the correct values) 3 pts each: (a) d/dx (e^xf(x)) when x=2 (b) d/dx (f(x)/g(x)) when x=1 (c) d/dx (ln(xf(x))) when x=1

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2...

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) = 2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the y-intercept of f, if any. (b) [3 marks] Find the horizontal and vertical asymptotes for the graph of y = f(x). (c) [4 marks] Determine the intervals where f is increasing, decreasing, and find the point(s) of relative extrema, if any....

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) -...

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f ″(x) - Determine any symmetry - Find the x- and y-intercepts - Use lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior - Locate any vertical asymptotes - Locate any horizontal asymptotes - Find all intervals where f (x) is increasing and decreasing - Find the open intervals where f (x) is concave up or concave down

Given f(x) = (x4 - 2)(x5 - 10x + 1)3 Find the definite integral of f(x)...

Given f(x) = (x4 - 2)(x5 - 10x + 1)3 Find the definite integral of f(x) on the closed interval [0, 1]. 1) 0.05 2) 204.75 3) 4095 4) None

consider the function f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2 a) find the local maximum and minimum...

consider the function f(x)=3x-5/sqrt x^2+1. given f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2 a) find the local maximum and minimum values. Justify your answer using the first or second derivative test . round your answers to the nearest tenth as needed. b)find the intervals of concavity and any inflection points of f. Round to the nearest tenth as needed. c)graph f(x) and label each important part (domain, x- and y- intercepts, VA/HA, CN, Increasing/decreasing, local min/max values, intervals of concavity/ inflection points of f?

Let F(x)=f(f(x)) and G(x)=(F(x))^2 . You also know that f(6)=14,f(14)=3,f′(14)=4,f′(6)=3. Find F′(6)= and G′(6)= .

Given: f (x) = (x − 2)/(x^2 − x +1)^2 a) Find the intervals where f(x)...

Given: f (x) = (x − 2)/(x^2 − x +1)^2 a) Find the intervals where f(x) is increasing, and decreasing b) Find the intervals where f(x) is concave up, and concave down c) Find the x-coordinate of all inflection points.

Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of...

Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x), and (f/g) (x). Give the domain of each. (f+g) (x) = (f-g)(x) = (fg)(x) = (f/g)(x) = The domain of f+g is_ The domain of f-g is_ The domain of fg is _ The domain of f/g is _ Please at the end provide showed work.

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