Use the previous exercise to show that f(x) = 1/x is not uniformly continuous on the interval (0, 1].
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Please solve question 9
![8. Suppose that SCR and that f : S → R is uniformly continuous. If xn € S is Cauchy,
then f(xn) is Cauchy.
9. Use the previous exercise to show that f(x)
interval (0, 1].
=
1/x is not uniformly continuous on the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2F86c885ca-ce8d-4f7a-a730-d769cacdab0b%2Fxmvwg6v_processed.jpeg&w=3840&q=75)
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- If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?1. Show (in terms of ε - δ) that a function f : R3 → R defined byf(x; y; z) = (2x + 3y + 4z) is uniformly continuous.Is g(x) = ln( x2+2 ) uniformly continuous on the interval (−∞,∞)?
- If I let f be continuously differentiable on R^2, how do I prove that gradf = (fx,fy)?If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the following is FALSE?Let Show that hn → 0 uniformly on R but that the sequence of derivatives (hn) diverges for every x ∈ R.
- Show that f(x) = 1 x is not uniformly continuous on (0,1) but it is uniformly continuous on [1,2]how (in terms of − δ) that a function f : R3 → R defined byf(x, y, z) = (2x + 3y + 4z) is uniformly continuousSuppose that w and r are continuous functions on (−∞, ∞), W (x) is an invertible antiderivative of w(x), and R(x) is an antiderivative of r(x). Circle all of the statements that must be true.
- Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]Let f : [0,∞) → R. Assume that f is uniformly continuous on [0, 1] andon [1,∞). Show that it is uniformly continuous on [0,∞)Find the value(s) of C in the given interval that satisfies the mean value Theorem for integral. f(x)= 1/x2 on [1,4]