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The function f : ℝ ℝ → satisfied  for all x, y ∈ and some constant c ∈ Then, 
  • a)
     f must be bounded 
  • b)
     f must be continuous but may not be uniformly continuous 
  • c)
     f must be uniformly continuous but may be not differentiable 
  • d)
     f must be differentiable
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The function f : → satisfiedfor all x, y ∈ and some consta...
The definition of lipschitz function is given by 
Let A R ⊆ and let f : A → ℝ if there exists a constant k > 0 such that 
so we have lipschitz function in our question asked (as it satisfies lipschitz condition) now we will show uniform continuity of lipschitz function 
Since 
The given ε > 0 we can take δ = ε/k if x. y ∈ ℝ satisfy ��-�� < δ
then, 
Therefore f is uniformly continuous on R 
But for differentiability
Since 
⇒ f is differentiable at y ∀ ∈ x,y ℝ
⇒ f is differentiable function to 0
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The function f : → satisfiedfor all x, y ∈ and some constant c ∈ Then,a)f must be boundedb)f must be continuous but may not be uniformly continuousc)f must be uniformly continuous but may be not differentiabled)f must be differentiableCorrect answer is option 'D'. Can you explain this answer?
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The function f : → satisfiedfor all x, y ∈ and some constant c ∈ Then,a)f must be boundedb)f must be continuous but may not be uniformly continuousc)f must be uniformly continuous but may be not differentiabled)f must be differentiableCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about The function f : → satisfiedfor all x, y ∈ and some constant c ∈ Then,a)f must be boundedb)f must be continuous but may not be uniformly continuousc)f must be uniformly continuous but may be not differentiabled)f must be differentiableCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f : → satisfiedfor all x, y ∈ and some constant c ∈ Then,a)f must be boundedb)f must be continuous but may not be uniformly continuousc)f must be uniformly continuous but may be not differentiabled)f must be differentiableCorrect answer is option 'D'. Can you explain this answer?.
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