Let f(x) be uniformly continuous and non-increasing on [0, 0). Assume that Jo f(x) dx < o. Prove the following assertions. (1) It holds f(x) > 0 for every x E [0, ∞). (2) It holds lim xf(x) = 0.

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A: Topic- Limits

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Q: 1. Suppose that f : [0, 0) → R is continuous and f(x) # 0 for all x > 0. If we have (f(x))? = 2…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: