SOLUTION: I am not sure how to work this out. I would appreciate any help. Thanks! Let "c" be a number and consider the function f(x) = { ax^2 -5, if x <1

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: I am not sure how to work this out. I would appreciate any help. Thanks! Let "c" be a number and consider the function f(x) = { ax^2 -5, if x <1       Log On


   

Question 944970: I am not sure how to work this out. I would appreciate any help. Thanks!
Let "c" be a number and consider the function f(x) = { ax^2 -5, if x <1
c, if x =1
(1/x)-2a, if x > 1 }

a) Find all numbers for "a" such that lim x-> 1 f(x) exists
b) Is there a number "c" such that f(x) is continuous at x=1?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For the limit to exist, f%28x%29 as you approach from the left (x%3C1) must equal f%28x%29 as you approach from the right x%3E=1.
ax%5E2-5=1%2Fx-2a
a%281%29%5E2-5=1%2F1-2a
a-5=1-2a
3a=6
a=2
.
.
.
For it to be continuous then,
c=2
That way the limit from the left, the limit from the right and the value at x=1 are all the same which is the definition of continuous.