Homepage › Solution manuals › Stephen Friedberg › Linear Algebra › Exercise 2.7.5

Exercise 2.7.5

Answers

If $f$ and $g$ are elements in $C^{\infty}$ , then we know that the $k$ -th derivative of $f + g$ exists for all integer $k$ since

{(f + g)}^{(k)} = f^{(k)} + g^{(k)} .

So $f + g$ is also an element in $C^{\infty}$ . Similarly, for any scalar $c$ , the $k$ -th derivative of $cf$ exists for all integer $k$ since ${(cf)}^{(k)} = c f^{(k)}$ . Finally, the function $f = 0$ is an element in $C^{\infty}$ naturally.

jephianlin

2011-06-27 00:00

Exercise 2.7.5

Answers

Comments

Add answer