From the given equation of h(x)
h(-1) = -1 (because -1 is in the first interval)
h(0.25) = 1 (because 0.25 is in the third interval)
h(2) = 2 (because -2 is in the fourth interval)
Suppose that the function h is defined on the interval (-2, 2] as follows. -1 if...
A function is defined as follows: y = X + 6 x² 3x + 1 X<-2 -2<x<3 x > 3 For which x-values is f(x) = 4? Select all that apply 0-2 1 2. 13 e here to search
Suppose that the functionſ is defined, for all real numbers, as follows. 3x+1 fx < -2 x-3 if x 2-2 Graph the functionſ. Then determine whether or not the function is continuous. Is the function continuous? 10 X o Yes NO O X ? 2 8 10 -10 Continue
Can you find a differentiable function f(x) defined on the interval [0, 3] such that , and for all x ∈ [0, 3]? Justify your answer (do not write only Yes or No, but explain your answer). We were unable to transcribe this imageWe were unable to transcribe this imagef'(x) <1
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
f(40) f(-3/2) f(-1) f(0) f(-3) Evaluate the piecewise defined function at the indicated values. if xs-1 if -1 <S1 x2 + 2x
Numerical analysis Question 1 A clamped cubic spline Six) on interval [0, 2) is defined by S(x) - 3 + ax + bx2 - 2x06x<1 (3 + c(x - 1) - 4(x - 1)2 + 7(x - 1) 1sx52 where a, b, care constants. Find the values of S'(0) and S(2).
х 0<I< 3. The tent function is defined by T(x) = 1 - < x < 1 2 otherwise (a) Express T(2) in terms of the Heaviside function. (b) Find the Laplace transform of T(x). (c) Solve the differential equation y" – y=T(x), y(0) = y'(0) = 0
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
1\x+21, x<0 -Sketch the graph of this piece-wise defined function: S(x) = {3 05x<2 1(x+1), x22
Sketch a graph of the piecewise defined function. sz if x <3 f(x) = x 1 if x 2 3