Don J.
asked • 11/22/17Choose the value of k that makes the following function continuous at x=1: help!?
f(x) =
1. -8x^2+48x-40/(x-1) x is less than 1
2. -2x+k x is greater than or equal to 1
More
1 Expert Answer
Michael J. answered • 11/22/17
Tutor
5
(5)
Mastery of Limits, Derivatives, and Integration Techniques
The function is continuous if the functions intersect at 1. First, we need to factor the first part.
(-8x2 + 48x - 40) / (x - 1) =
-(8x2 - 48x + 40) / (x - 1) =
-8(x2 - 6x + 5) / (x - 1) =
-8(x - 1)(x - 5) / (x - 1) =
-8x + 40
Now we set this equal to (-2x + k) at x=1.
-8(1) + 40 = -2(1) + k
Solve for k. I live this part up to you.
Still looking for help? Get the right answer, fast.
Ask a question for free
Get a free answer to a quick problem.
Most questions answered within 4 hours.
OR
Find an Online Tutor Now
Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.
Andrew M.
Remember that dividing by zero is undefined.. We cannot divide by zero,
which means a function cannot have zero in the denominator.
There is no "k" in your first expression:
-8x^2+48x-40/(x-1) x is less than 1
but this is not continuous at x=1 because that would make the denominator zero.
2. -2x+k x is greater than or equal to 1
This is continuous for any real value of k
11/22/17