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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]
@@ Line 7: / Line 7: @@
 Exercises:
   * 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 $x \in (0,1)$.
-  * 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

Lecture Notes