Mathematics · Real Analysis
Let f(x) = e x for x ∈ ℝ. Which of the following statements is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1There is a real C > 0 such that |f(x) - 1 - x - x 2 2 - x 3 3! | ≤ Cx 4 for all x ∈ [-1, 1]✓
- 2There is a real C > 0 such that |f(x) - 1 - x - x 2 2 - x 3 3! | ≤ Cx 4 for all x ∈ ℝ
- 3There is a real C > 0 such that |f(x) - 1 - x - x 2 2 | ≤ C|x| 3 for all x ∈ [-1, 1]
- 4There is a real C > 0 such that |f(x) - 1 - x| ≤ Cx 2 for all x ∈ ℝ
Correct answer
There is a real C > 0 such that |f(x) - 1 - x - x 2 2 - x 3 3! | ≤ Cx 4 for all x ∈ [-1, 1]
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