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Section 1.3 3. For each of the following, determine algebraically whether function is even, odd, or...
Determine algebraically whether the given function is even, odd, or neither. h(x)= 3x²+4 O Neither Even Odd
Determine algebraically whether the function is odd, even, or neither. g(x) = -5x4 - 3x2 +9 O Odd, g(-x) = -g(x) O Even, g(-x) = g(x) Odd, g(-x) = g(x) O Neither even nor odd Even, g(-x) = -g(x)
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
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
Section 2.6 Homework (continued) D. Determine the end behavior of the following function. (Do this algebraically.) $ 16x8 – 12x2 f(x) = 1- 7x² + 5x 70 + 2X-8 C. Find the limit or show that it does not exist. (a.) lim n sin²x " (Hint: Use squeeze theorem) X x²+1 (b.) lim cot?(-Inx) (Do this analytically.) X-> Section 2.6 Homework (continued) E. Find the following limits if they exist. Explain. (Do this analytically (a.) lim cot' (In 10 -...
Determine whether the functions are even, odd, or neither.(a) f(x) = x²/√x²+ 1(b) g(x) = x^3 - √ x- 7
1. Cousider the followving periodic function a) Determine whether the following function is odd, even or neither f(x) = sin 2x cos 3a. 2marks] Consider the following periodic function b) ㄫㄨ for -2 < x < 0 for 0< S 2 f(x) = { sin 0 f(x) = f(x + 4). i. Sketch the graph of the function over the interval-6< r <6. 2marks] Find the Fourier Series of f(x). (6marks ii.
Discuss the symmetry of the graph of the function, and determine whether the function is even, odd, or neither. f(x) = 4x + 4x6 LY X 10 10 This graph is O A. symmetric about the y-axis. B. not symmetric about either. O C. symmetric about the x-axis. -16 This function is O A. odd. O B. even. C. neither
Discuss the symmetry of the graph of the function, and determine whether the function is even, odd, or neither f(x) = 4x + 4x® This graph is A. symmetric about the y-axis. OB. not symmetric about either. OC. symmetric about the x-axis. -10 10 This function is O A odd. 10 OB. even O c. neither
Use possible symmetry of the graph to determine whether it is the graph of an even function, an odd function, or a function that is neither even nor odd. -5-4-3-2/14 1 2 3 4 2 13- bu O The function is even. O The function is odd. O The function is neither even nor odd. AY Use the graph to determine a. the function's domain; b. the function's range; c. the x-intercepts, if any; d. the y-intercept, if any, and...