Let S = {−1, 0, 2, 4, 7}, find f(S) if 1. f(x) = 1 2....
Let S = {−1, 0, 2, 4, 7}, find f(S) if
1. f(x) = 1
2. f(x) = 2x + 1
3. f(x) = bx/5c
4. f(x) = d(x 2 + 1)/3e
Homework Answers
1. f(x) = 1
Explanation: Output is 1 irrespective of of the value of x.
2. f(x) = 2x+1
Explanation: Put each value in set and evaluate.
x = -1 --> 2 * ( - 1 ) + 1 --> - 2 + 1 --> -1
x = 0 --> 2 * ( 0 ) + 1 --> 0 + 1 and so on for other values in S.
3. f(x) = bx/5c
Explanation : Here b and c are contant values as will be provided.
x = -1 --> b * (-1) / 5c --> -b / 5c
x = 0 --> b * (0) /5c --> 0 and so on for other values.
4. f(x) = d(x^2+1)/3e
Explanation : Here d and e are contant values.
x = -1 --> d ( (-1)^2 +1 ) / 3e --> d( 1 + 1) / 3e --> 2d/3e and so on for other values.
The table for all the values in S is as shown below along with mapping as per f(x).
| x; x E S | f(x) = 1 | f(x) = 2x + 1 | f(x) = bx/5c | f(x) = d(x^2 + 1)/3e |
| -1 | 1 | -1 | -b/5c | 2d/3e |
| 0 | 1 | 1 | 0 | d/3e |
| 2 | 1 | 5 | 2b/5c | 5d/3e |
| 4 | 1 | 9 | 4b/5c | 17d/3e |
| 7 | 1 | 15 | 7b/5c | 50d/3e |
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let f:[-pi,pi] -> R be definded by the function f(x) { -2 if -pi<x<0 2 if...
let f:[-pi,pi] -> R be definded by the function f(x) { -2
if -pi<x<0 2 if 0<x<pi
a) find the fourier series of f and describe its convergence
to f
b) explain why you can integrate the fourier series of f term
by term to obtain a series representation of F(x) =|2x| for x in
[-pi,pi] and give the series representation
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7. (10) If 1+ f(x) + x' [f(x)] = 0, and f(1) = 2, find f'(1). 8. (10) Differentiate the function 9. (10') Find an equation of the tangent line to the curve y=9-2x at the point (2,1)
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7 7. Let Xi, . . . , xn be iid based on f(x:0) = 2x e-x2/0 where x > 0, Show that θ =「X 2 is 2-1 efficient.
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Let f(t) = 2t + 4. f-1(s) Let g(x) 2 + 1 g-(3) Below is an input-output table for the function h(x). х h(x) 2 0 1 1 2 الها 3 1 4 0 h-(3) = Now consider the following graph: 5 3 2 -5 -4 -3 -2 -/ 2 Cat 3 4. -2 3 -4 -5+ q
These are linear algebra problems.
1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
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Problem 4 Let S :R R be such that f (x + y) = f(x) + f(y) for all sy ER Also assume that limf () = LER. 1. Show that f (2x) = 2 (s). 2. Use the result from part 1 to determine the value of L.
let f:[-pi,pi] -> R be definded by the function f(x) { -2
if -pi<x<0 2 if 0<x<pi
a) find the fourier series of f and describe its convergence
to f
b) explain why you can integrate the fourier series of f term
by term to obtain a series representation of F(x) =|2x| for x in
[-pi,pi] and give the series representation
DO - - - 1. Let f: [-T, 1] + R be defined by the function S-2 if-A53 <0...
7. (10) If 1+ f(x) + x' [f(x)] = 0, and f(1) = 2, find f'(1). 8. (10) Differentiate the function 9. (10') Find an equation of the tangent line to the curve y=9-2x at the point (2,1)
7. (10) If 1+ f(x) + x' [f(x)] = 0, and f(1) = 2, find f'(1). 8. (10) Differentiate the function 9. (10') Find an equation of the tangent line to the curve y=9-2x at the point (2,1)
7 7. Let Xi, . . . , xn be iid based on f(x:0) = 2x e-x2/0 where x > 0, Show that θ =「X 2 is 2-1 efficient.
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