anonymous
  • anonymous
Does anyone know why the function f(x)= 1/(x-1)^4 the limit as it approaches to 1 is infinite. I thought that in this case we should use the one-side limits because when x=1 the denominator will be 0.
OCW Scholar - Single Variable Calculus
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
phi
  • phi
if you get the same value for both the left and right-sided limit, then that value is the limit. In this case approaching from the left side of 1 (below 1) \[\lim_{x \rightarrow 1^-} \frac{ 1 }{ (x-1)^4 }=\frac{ 1 }{ 0 }= \infty\] notice that though 0.999-1.000 = -0.001 is negative, after raising to an even power (4 in this case) we get a positive number that approaches 0 similarly, the other side also gives \[\lim_{x \rightarrow 1^+} \frac{ 1 }{ (x-1)^4 }=\frac{ 1 }{ 0 }= \infty\] example: 1.001 -1.000= 0.001, and raised to the 4th power, is a small positive number that approaches 0, and consequently the fraction approaches infinity.

Looking for something else?

Not the answer you are looking for? Search for more explanations.