math104-s22:hw:hw9
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math104-s22:hw:hw9 [2022/04/08 13:28] pzhou created |
math104-s22:hw:hw9 [2022/04/13 17:41] (current) pzhou [HW 9] |
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| * Read Ross p257, Example 3 about smooth interpolation between $0$ for $x \leq 0$ and $e^{-1/x}$ for $x>0$. Construct a smooth function $f: \R \to \R$ such that $f(x)=0$ for $x\leq 0$ and $f(x)=1$ for $x\geq 1$, and $f(x) \in [0,1]$ when $x \in (0, | * Read Ross p257, Example 3 about smooth interpolation between $0$ for $x \leq 0$ and $e^{-1/x}$ for $x>0$. Construct a smooth function $f: \R \to \R$ such that $f(x)=0$ for $x\leq 0$ and $f(x)=1$ for $x\geq 1$, and $f(x) \in [0,1]$ when $x \in (0, | ||
| - | * Rudin Ch 4, Ex 4 (hint: apply Rolle mean value theorem to the primitive) | + | * Rudin Ch 5, Ex 4 (hint: apply Rolle mean value theorem to the primitive) |
| - | * Rudin Ch 4, Ex 8 (ignore the part about vector valued function. Hint, use mean value theorem to replace the difference quotient by a differential) | + | * Rudin Ch 5, Ex 8 (ignore the part about vector valued function. Hint, use mean value theorem to replace the difference quotient by a differential) |
| - | * Rudin Ch 4, Ex 18 (alternative form for Taylor theorem) | + | * Rudin Ch 5, Ex 18 (alternative form for Taylor theorem) |
| - | * Rudin Ch 4, Ex 22 | + | * Rudin Ch 5, Ex 22 |
math104-s22/hw/hw9.1649449737.txt.gz · Last modified: 2022/04/08 13:28 by pzhou
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