Go Help we ar given a funchon f (x) = sin 2x 2 ing a Calculate he cosive sevies IT ntervs Sketch the even extend ,f -IT, TT) Go Help we ar given a funchon f (x) = sin 2x 2 ing a Calculate he...
1. Determine whether the function f(x) = (x2 - 1) sin 5x is even, odd, or neither. A. Even B. Odd C. Neither 2. a). Find the Fourier sine series of the function f(x) shown below. b). Sketch the extended function f(x) that includes its two periodic extensions. TT/2 TT Formula to use: The sine series is f(x) = 6 sin NIT P where b. - EL " (x) sin " xd
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o D. go Given y=f(u) and u = g(x), find dy/dx = f(g(x))g'(x). y = sin u, u = 2x + 12 Select one: A. 2 cos (2x + 12) B. cos (2x + 12) C. - 2 cos (2x + 12) D. - cos (2x + 12)
2. The function of f(x) is given by TT X+ - 1<xs- 2 7 π -X, <x< 2 2 π X-TT, f(x)= <x<s, 2 f(x+27). a) Sketch the graph of f(x) for the range -1<x<. b) Based on a), determine the type of function f (x) and state your reason. c) Find the Fourier series of f(x).
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MHF 401 Page 5 1 9. For f(x) = sin(2x + 2) +2: (4 marks) (a) Complete a table of values for the "key" points. (c) Write a mapping formula. (e) Sketch the new graph. (b) Sketch the starting function. (d) Determine the translated "key" points. (a) (d) 1x) = sinx x) 0 JI 2 TT 3 2 2 T (c)(x, y) - 11. Prove: sinxtanxsex-cos X
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
sin (x - 1) x-TT x <T Given f(x) = x2 · Tex + 1, x > Determine if the graph is continuous at it (Show all work)
1. [8] Given x + 2, -2 < x < 0 f(x) = 12 – 2x, 0<x< 2, f(x + 4) = f(x) (a)[3] Sketch the graph of this function over three periods. Examine the convergence at any discontinuities (b)[5] Find the Fourier series of f(x) 2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods...
Given, f(x) = {x +1,25x<4 4,0<x<2 (a) Sketch the graph of f(x) and its even half-range expansion. Then sketch THREE (3) full periods of the periodic function in the interval – 12 < x < 12. (6 marks) (b) Determine the Fourier cosine coefficients of Ql(a). (10 marks) (c) Write out f(x) in terms of Fourier coefficients you have found in Q1(b). (4 marks)
Given the function f(x) and its derivative f'(x). F"(7), sketch the graph of f(x). If applicable, identity local extremum, points of inflection, asymptotes, and intercepts. (1) f(a) == (2) f(x) = f(a) = (-1)"(t) = , f'(x) = -2° +8 f"(ar) = 24 (3) f(x) = (4) f(x) = r - 2 sin 2, 3 VI f'(x) = 1 - 2 cos z f"(x) = 2 sina,
x? - 2x+1 7. (15) Given the function f(x) (x-1)2 calculate all possible intercepts, X asymptotes, and relative max and min points. Draw a sketch of the graph.