it is not at all clear what function you are taking the limit ofI need help finding the limit of the following. lim ( x - 1 - 1 )
x--> 1 2x-2 X^2
could you resubmit to clarify this?
I need help finding the limit of the following. lim ( x - 1 - 1 )
x--> 1 2x-2 X^2
I am having trouble with the algebra. The limit of a rational function is found by substitution. But in the case of an indeterminate as this one I must factor, rationalize, combine rational expressions, etc... to simplify into an equivalent function. Then find the limit of the equivalent function by substitution. Can someone please help. I have been trying to figure this out for about six hours. Is there a method that I am unaware of for finding the common denominator and subtracting these three expressions so I can sunstitute and get the limit. My calculator soves the problem but I need to know how to do it by hand.
The exercise in my text says to find the limit algebraically. the problem is: lim as x approaches 1 then the quantity (x/2x-2 minus 1/x^2 minus 1). The answer in the back of the book is 3/4. The answer I get on my ti-89 titanium is -7/2. Hope this clarifies. Thanks for your time.
I think you mean but that's easy: the numerator on the first fraction goes to 1 as does the denominator so its limit is 1. The second fraction has numerator 1 while the denominator goes to 1 so its limit is also 1. The limit of the difference is 1- 1= 0.
Three expressions? Is it or img.top {vertical-align:15%;} \frac{x}{2x}- \frac{1}{2x^2}= \frac{x^2- 1}{2x^2}" alt="\lim_{x\to 1}\frac{x}{2x}- \frac{1}{2}- \frac{1}{x^2} \frac{x}{2x}- \frac{1}{2x^2}= \frac{x^2- 1}{2x^2}" /> which, at x= 1, is 0 so the limit of the entire thing is 1. If the latter, then [tex]\frac{x}{2x}- \frac{1}{2}- \frac{1}{x^2}= \frac{x^2- x^2- 2}{x^2}= \frac{2}{x^2}[/itex] and that is 2 at x= 1.I am having trouble with the algebra. The limit of a rational function is found by substitution. But in the case of an indeterminate as this one I must factor, rationalize, combine rational expressions, etc... to simplify into an equivalent function. Then find the limit of the equivalent function by substitution. Can someone please help. I have been trying to figure this out for about six hours. Is there a method that I am unaware of for finding the common denominator and subtracting these three expressions so I can sunstitute and get the limit. My calculator soves the problem but I need to know how to do it by hand.
I can see no "indeterminate" form in any of these. If you can't use LaTex, please use parentheses to make clear exactly what numerators and denominators the fractions have.
HALLSOFIVY, yes, the limit is the three as you described it. I will learn how to use the latex but until then I will use the parenthesis as you stated. the limit as x appraoches 1 is the three rationals ((x/2x-2) - (1/x^2) - 1). All three inside a parenthesis.