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HOMEWORK 4 (due Oct. 1). Hatremnntien Consider the discrete model x f(x,)where f(x,) g(x,) * g(x,)=...
*PLEASE DO IN MATHEMATICA* {:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of the derivative and LHo...
*PLEASE DO IN MATHEMATICA*
{:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of the derivative and LHopital's Rule to show that every higher-order derivative of f at r 0 vanishes. c. Find the MacLaurin series for f. Does the series converge to f?
{:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of...
(3) Consider f: R3- R3 defined by (u,, w)-f(r, y, :) where u=x w = 3~....
(3) Consider f: R3- R3 defined by (u,, w)-f(r, y, :) where u=x w = 3~. Let A = {1 < x < 2, 0 < xy < 2, 0 < z < 1). Write down (i) the derivative Df as a matrix (ii) the Jacobian determinant, (ii) sketch A in (x, y. :)-space, and iv) sketch f(A) in (u. v, w)-space.
Homework 19. Due April 5. Consider the polynomial p(z) = r3 + 21+1. Let F denote the field Q modu...
Homework 19. Due April 5. Consider the polynomial p(z) = r3 + 21+1. Let F denote the field Q modulo p(x) and Fs denote the field Zs[r] modulo p(x). (i) Prove that p(x) is irreducible over Q and also irreducible over Zs, so that in fact, F and Fs are fields (ii) Calculate 1+2r2-2r + in HF. (iii) Find the multiplicative inverse of 1 +2r2 in F. (iv) Repeat (ii) and (iii) for Fs. (v) How many elements are in...
I need help with my discrete math question. thanks in advance Let f(x) = 0 +...
I need help with my discrete math question. thanks in
advance
Let f(x) = 0 + 0,-1-1...+ar+ao with 00, 01,..., an being real numbers. Prove that f(0) E O(") by finding a pair of witnesses C and k such that f(x) < Cx" whenever I k.
1) Let f(x) = 1 sin x, x E R , and consider the discrete-time dynamics...
1) Let f(x) = 1 sin x, x E R , and consider the discrete-time dynamics given by xn+1 = f(xn), n = 0.1, 2, . . . How many fixed points are there? Stable or unstable?
Let y'(x)y(x)g'(x) = g(x)g'(x), y(0) = 0, x e í, where f'(x) denotes ar(X) and g(x) is a given non- 4....
Let y'(x)y(x)g'(x) = g(x)g'(x), y(0) = 0, x e í, where f'(x) denotes ar(X) and g(x) is a given non- 4. dx constant differentiable function on R with g(0) = g(2) = 0. Then find the value of y(2)
Let y'(x)y(x)g'(x) = g(x)g'(x), y(0) = 0, x e í, where f'(x) denotes ar(X) and g(x) is a given non- 4. dx constant differentiable function on R with g(0) = g(2) = 0. Then find the value of y(2)
Homework in statistics ariant 14 1. Discrete distribution for X is given by the following table:...
Homework in statistics ariant 14 1. Discrete distribution for X is given by the following table: Probabilities p Values X 0.2 40 0.1 0.5 4 0.1 50 0 20 10 20 Find distribution function fx) and median Me(x). Calculate expectation value (dispersion) D(X), standard error σ(X) , asymmetry coefficient As(X) and excess Ex(X) Mx), variance 2. Calculate multiplier k. Find distribution function fitz, mode Moty), median Meco, expectation M(x), variance (dispersion) D(x), standard error σ( for continuous distributions with the...
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to...
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to the function f at a = (ii) Graph f and L on the same set of axes. (iii) Based on the graphs of part (ii), state whether linear approximations to f near a are underestimates or overestimates. (iv) Compute f"(a) to confirm your conclusion.
1) Let f:R-->R be defined by f(x) = |x+2|. Prove or Disprove: f is differentiable at...
1) Let f:R-->R be defined by f(x) = |x+2|. Prove or Disprove: f is differentiable at -2 f is differentiable at 1 2) Prove the product rule. Hint: Use f(x)g(x)− f(c)g(c) = f(x)g(x)−g(c))+f(x)− f(c))g(c). 3) Prove the quotient rule. Hint: You can do this directly, but it may be easier to find the derivative of 1/x and then use the chain rule and the product rule. 4) For n∈Z, prove that xn is differentiable and find the derivative, unless, of course, n...
1. Give a complete list of all numbers a for which z2 +1 > ar. 2....
1. Give a complete list of all numbers a for which z2 +1 > ar. 2. Definition: A function f is even if f(-x) = f(x) for all inputs z. A function f is odd if f(-x) = -f(x). (a) Let f be any function with domain (-0,0). i. Show that the function g(x) = f(x) + f(-x) is even. ii. Show that the function h(x) = f(0) - f(-x) is odd. iii. Show that f can be written as...
*PLEASE DO IN MATHEMATICA*
{:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of the derivative and LHopital's Rule to show that every higher-order derivative of f at r 0 vanishes. c. Find the MacLaurin series for f. Does the series converge to f?
{:1, ifr+ 13. Consider the function f(x)- nction,f(x)-e-r/rifx#0 a. Plot the graph of this function using Mathematica. b. Use the limit definition of...
(3) Consider f: R3- R3 defined by (u,, w)-f(r, y, :) where u=x w = 3~. Let A = {1 < x < 2, 0 < xy < 2, 0 < z < 1). Write down (i) the derivative Df as a matrix (ii) the Jacobian determinant, (ii) sketch A in (x, y. :)-space, and iv) sketch f(A) in (u. v, w)-space.
Homework 19. Due April 5. Consider the polynomial p(z) = r3 + 21+1. Let F denote the field Q modulo p(x) and Fs denote the field Zs[r] modulo p(x). (i) Prove that p(x) is irreducible over Q and also irreducible over Zs, so that in fact, F and Fs are fields (ii) Calculate 1+2r2-2r + in HF. (iii) Find the multiplicative inverse of 1 +2r2 in F. (iv) Repeat (ii) and (iii) for Fs. (v) How many elements are in...
I need help with my discrete math question. thanks in
advance
Let f(x) = 0 + 0,-1-1...+ar+ao with 00, 01,..., an being real numbers. Prove that f(0) E O(") by finding a pair of witnesses C and k such that f(x) < Cx" whenever I k.
1) Let f(x) = 1 sin x, x E R , and consider the discrete-time dynamics given by xn+1 = f(xn), n = 0.1, 2, . . . How many fixed points are there? Stable or unstable?
Let y'(x)y(x)g'(x) = g(x)g'(x), y(0) = 0, x e í, where f'(x) denotes ar(X) and g(x) is a given non- 4. dx constant differentiable function on R with g(0) = g(2) = 0. Then find the value of y(2)
Let y'(x)y(x)g'(x) = g(x)g'(x), y(0) = 0, x e í, where f'(x) denotes ar(X) and g(x) is a given non- 4. dx constant differentiable function on R with g(0) = g(2) = 0. Then find the value of y(2)
Homework in statistics ariant 14 1. Discrete distribution for X is given by the following table: Probabilities p Values X 0.2 40 0.1 0.5 4 0.1 50 0 20 10 20 Find distribution function fx) and median Me(x). Calculate expectation value (dispersion) D(X), standard error σ(X) , asymmetry coefficient As(X) and excess Ex(X) Mx), variance 2. Calculate multiplier k. Find distribution function fitz, mode Moty), median Meco, expectation M(x), variance (dispersion) D(x), standard error σ( for continuous distributions with the...
(4) Consider the function f(x) = V2 cos x. (1) Find the linear approximation L to the function f at a = (ii) Graph f and L on the same set of axes. (iii) Based on the graphs of part (ii), state whether linear approximations to f near a are underestimates or overestimates. (iv) Compute f"(a) to confirm your conclusion.
1. Give a complete list of all numbers a for which z2 +1 > ar. 2. Definition: A function f is even if f(-x) = f(x) for all inputs z. A function f is odd if f(-x) = -f(x). (a) Let f be any function with domain (-0,0). i. Show that the function g(x) = f(x) + f(-x) is even. ii. Show that the function h(x) = f(0) - f(-x) is odd. iii. Show that f can be written as...
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