Correct answer: (D) If f is continuous and has a finite limit at infinity,then f is uniformly continuous.
Explanation
D follows by controlling the tail using the finite limit and the remaining compact interval using uniform continuity there. A fails for sin(x²). B fails for sin x. C fails for f(x)=x,which is uniformly continuous,but x sin x has fixed output changes across shrinking input gaps near 2πn. **D**.
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