Let f (x) = 1/x sin 1/x , for x not = 0.– Let xn = 1/n π^2. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.– Is f continuous at 0? Justify.– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?– Can f be redefined at 0 so that it’s continuous on R? Justify

Let f (x) = 1/x sin 1/x , for x not = 0.– Let xn = 1/n π^2. What is limn→∞ xn? limn→∞ sin( 1/xn )? limn→∞ f (xn)? Justify.– Is f continuous at 0? Justify.– In the definition of f (x) above, f (x) is not assigned a value at x = 0. Redefine f (x)as follows: f (x) = 1/x sin 1/x , for x is not equal to 0 and f (0) = 0. Is f (x) continuous at 0? Why?– Can f be redefined at 0 so that it’s continuous on R? Justify

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

See similar textbooks