Calculus - limitsDate: 12/10/95 at 22:47:46 From: Anonymous Subject: Calculus - limits Question: I need some help with this. We have gone far in this semester in calculus, but I have forgot how to do this. Thankyou in advance for any suggestions you may give. Find all the discontinuities of the following function and label those that are removable. Given this piece-wise function. | _________ | \/ x^4 + 1 if x < 0 | | 7 if x = 0 | | _____5_____ | _______ if 0 < x < 11 | \/ 25 + x | f(x)= | | __5__ if x = 11 | 6 | | __(x-6)(x-13)__ if x > 11 | 6x - 78 | I know that you have to find certain conditions to make the function continuous. There are several rules that must happen if a function is continuous. 1. Limit must exist. 2. Left limit must = right limit. 3. f(c) = limit (I think) How do you find the discontinuities and if they are removable ? Thanks again for any help. Simon B. Smith Date: 7/23/96 at 20:45:41 From: Doctor Jerry Subject: Re: Calculus - limits Your comments 1, 2, 3 at the end of your note are correct. At x=0, the function is 7 and both one-sided limits are equal to 1. If we are allowed to redefine the function to be 1 at 0, then we can make the slightly different function continuous at 0. Otherwise, the function as originally defined at 0 is not continuous. At 11 both one-sided limits are equal to 5/6, which is the function value there. Hence it is continuous. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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