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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) ?for part a, did u show that f' is not continuous? and i dont really get how it proves differentiabilityalso for part c, does lipchitz continuous mean uniformly continous, and if so can you define lipchitz continousSuppose f is continuous on [0, ∞) and limx→∞ f (x) = 1 . Is itpossible that ∫ 0∞f (x) dx is convergent?
- 4. Determine whether or not the following functions are uniformly continuous.(Use ε and δ to prove your work through e delta definition) Kindly do only a,b and c but do ASAP4. Determine whether or not the following functions are uniformly continuous.(Use ε and δ to prove your work through e delta definition) and do only d and e please ASAPSuppose f is continuous on [0 , infinity) and limit x appraoaches infinity f(x) =1. Is itpossible that integral 0 to infinity f(x) dx is convergent
- Suppose f '' is continuous on (−∞, ∞). (a) If f '(−3) = 0 and f ''(−3) = 7, what can you say about f ? At x = −3, f has a local maximum. At x = −3, f has a local minimum. At x = −3, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = −3. (b) If f '(1) = 0 and f ''(1) = 0, what can you say about f ? At x = 1, f has a local maximum. At x = 1, f has a local minimum. At x = 1, f has neither a maximum nor a minimum. More information is needed to determine if f has a maximum or minimum at x = 1.5. Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?4. Determine whether or not the following functions are uniformly continuous.(Use ε and δ to prove your work through e delta definition)
- I need help with #1 and #2 using the given definition of uniformly continuous.Answer true or false. If f is not piecewise continuous on [0, ∞>), then ℒ{f(t)} will not exist.Suppose f(x) is continuous on [0, 1], with f(0) = 2 and f(1) = 0. Then there must be a value x in [0, 1] for which f(x) = 1. Why?