Is f(x) = sin(x)/x2 on (0,1) uniformly continuous?
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Is f(x) = sin(x)/x2 on (0,1) uniformly continuous?
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- The sketch that represents a continuous function, y = f(x), such that: * (-3) = 5 and f'(- 3)=Ø f(1) = 2 and f'(1)=0 is А. C. (-3,5) (-3,5) (1, 2) (1, 2) В. D. (-3,5) (-3, 5) (1.2) (1,2) B.Describe the long run behavior of f(x) = x* As x → o, f(x) → ? As x → 0, f(x) → ?Estimate f(x) dx given that f is a continuous function containing (-2, 8), (–1,0), (4, 125) , and points of the form (x, e") for all positive integers x using an appropriate Newton-Cotes quadrature rule utilizing all the given data in this problem.
- We are given the following functionsf : Z → Z × Z, f(x) = (x^2, x^3). (a) Find images f({1, 2, 3}) and f(N).(b) Find those preimages f^−1({1, 2, 3, 4}) and f^−1({(1, −1),(4, 8)}) that are welldefined.Determine whether the functions are linearly dependent or linearly independent on the specified intervals: (a){e*,e*,e*} on(-w,00) (b){x',x² -1,5} on(-,00) (c){sin² x,cos' x,1} on(-0,) (d){sin² x,cos? x, cos 2.x}on(-0, 00)Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]