Exercise · ZW-SMOOTH-FUNCTION-002 · ★☆☆ Basic
Which of these functions from \(\mathbb{R}\) to \(\mathbb{R}\) is smooth?
Choose one option.
Show answer
- A. \(e^{x}\)
Explanation
\(e^{x}\) has derivatives of all orders on \(\mathbb{R}\). The others are not differentiable at \(0\).
Review the concept: Smooth function
A smooth function is a function between spaces with differentiable structure that, written in local coordinates, has derivatives of all orders.
\[f\in C^{\infty}(M,N)\]
More practice problems: smooth function
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- ZW-SMOOTH-FUNCTION-007 If f and g from ℝ to ℝ are smooth, what can be said about g∘ f?
- ZW-SMOOTH-FUNCTION-008 Let f(x)=x^2sin (1/x) for xne 0 and f(0)=0. Which statement is correct?
- ZW-SMOOTH-FUNCTION-009 What is a diffeomorphism between two smooth manifolds?