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Show that |2𝜋-2𝜋x2sin8 (𝑒 𝑥 ) 𝑑𝑥| ≤ 16𝜋 3/ 3 .
discuss the continuity/uniform continuity/Lipchitz continuity and differentiability of the functions 3√𝑥 on [−1,1].
discuss the continuity/uniform continuity/Lipchitz continuity and differentiability of the functions |x| on [−1,1].
Discuss the continuity/uniform continuity/Lipchitz continuity and differentiability of the functions |𝑥|, |𝑥| 3 , √𝑥 3 on [−1,1].
Discuss the continuity/uniform continuity/Lipchitz continuity and differentiability of the functions |𝑥|, |𝑥| 3 , √𝑥 3 on [−1,1]
Discuss the continuity/uniform continuity/Lipchitz continuity and differentiability of the functions |𝑥|, |𝑥| 3 ,3 √𝑥 on [−1,1].
Discuss the continuity/uniform continuity/Lipchitz continuity and differentiability of the functions |𝑥|, |𝑥| 3 , √𝑥 3 on [−1,1].
Show that the function defined as 𝑓(𝑥) = { 𝑥, 𝑥 ∈ ℚ
𝑥 2 , 𝑥 ∈ ℝ − ℚ
is continuous at 1 and discontinuous at 2.
State, prove and give an example of one-sided versions of the Sandwich theorem corresponds to 𝑓(𝑥) → ∞ and 𝑓(𝑥) → −∞.
Show that the function defined as 𝑓(𝑥) = { 𝑥, 𝑥 ∈ ℚ
𝑥 2 , 𝑥 ∈ ℝ − ℚ is continuous at 1 and discontinuous at 2.
