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1 Define the concept of functions 2. Consider the function f(x)=x-x+S. (2) f(0) (1) 3. Consider...
1\x+21, x<0 -Sketch the graph of this piece-wise defined function: S(x) = {3 05x<2 1(x+1), x22
The function shown below is described by: f(x) 1 when 0sx<1 0 f(x)-when 1sx<2 X 3 f(x) 0 when x22 Sketch a graph of the function: Ix)()dt
We define a function by: and we suppose that f (x + 2) = f (x) for all x ∈ R. (a) Draw the graph of the function f (x) over the interval [−3, 3]. (b) Find the Fourier series for the function f (x). f(x) = { x +1 si -1 < x < 0; si 0 < x <1, 1
(1 point) Consider the function f(x) = xe-5x, 0<x< 2. This function has an absolute minimum value equal to: which is attained at x = and an absolute maximum value equal to: 1/(5e) which is attained at x =
Consider the function S Ax? f(x) = - { x < 3 17 - Ax x3 Find a value of A so that the function is continuous at x = 3. - 12/17 17/12 12/17 17/3 - 17/12
Consider the function f(0) = 2x3 + 6x² – 144x +1 with -6<< < 5 This function has an absolute minimum at the point and an absolute maximum at the point Note: both parts of this answer should be entered as an ordered pair, including the parentheses, such as (5, 11). į < x < 5. Consider the function f(1) = 1 – 2 In(x), The absolute maximum value is and this occurs at x equals The absolute minimum value...
Define the density function (f(x)) as below: f(x) = cx'for 0<x<2,0 otherwise Where c was determined above. What is the probability this random variable takes a value between 1 and 1.5?
Step functions can be used to define a window function. Thus u (t + 2) – u(t – 3)f (t) f(t) = 0, t<0 5t, 0<t<10 s -5t+100, 10 s <t < 30 s = -50, 30 s <t < 40 s 2.5t - 150 40 s <t <60 = 0, 60 s <t< oo - Part A Sketch f(t)0 s <t < 60 s ) graph of f versust No elements selected + t) 3040 Part B Use the...
2. Consider the cubic spline for a function f on [0, 2] defined by S(x) = { ={ (z. 2x3 + ax2 + rx +1 if 0 < x <1 (x - 1)3 + c(x - 1)2 + d(x - 1) + ß if 1 < x < 2 where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
(6 pts) Consider the joint density function f(x, y) = { (9- 2- y), 0<r<3, 3 Sy <6, 0, otherwise Find P(0 < < <1,4 <y<6).