amonoconnor
  • amonoconnor
I have a question regarding Limits & Continuity of functions. The problem I'm stuck on is... "For what values of the constant "c" is the function "f" continuous on (-∞ ,∞ )? f(x) = [cx^2 + 2x, if x<2] and [x^3 - cx, if x ≥ 2]. Any and all help is greatly appreciated!
Calculus1
  • 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!
anonymous
  • anonymous
Both parts of f(x) are polynomials, so you only need to make sure they have the same value for f(2). Plug in 2 for x and set the two parts equal to solve for c 4c + 4 = 8 - 2c
amonoconnor
  • amonoconnor
The first function isn't continuous at x=2 though, correct? The second one is continuous from the right? Also, so we solve for "c" by setting the polynomials equal to each other and plugging in the 'conditional' values, and that is the answer to the problem? The "values of the function where "f" is continuous from (-∞ ,∞ )? It's that simple? :)
amonoconnor
  • amonoconnor
Sorry if my responses are slow... dorm wifi is crapping out here :p

Looking for something else?

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

More answers

anonymous
  • anonymous
sorry I'm also having trouble on my end
anonymous
  • anonymous
What I meant was that the functions are both continuous at x = 2 when they aren't a part of a piecewise function, so there are no other discontinuities to consider except the one at x = 2. Just plug in 2 for x to solve for c. If you need to prove continuity, you'd take the limits on each side and they'd have to equal f(2)

Looking for something else?

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